diff --git a/packages/eslint-plugin/README.md b/packages/eslint-plugin/README.md
index 19ee2638a8e7..a14b3ced2fd5 100644
--- a/packages/eslint-plugin/README.md
+++ b/packages/eslint-plugin/README.md
@@ -132,6 +132,7 @@ Pro Tip: For larger codebases you may want to consider splitting our linting int
 | [`@typescript-eslint/no-unnecessary-qualifier`](./docs/rules/no-unnecessary-qualifier.md)                             | Warns when a namespace qualifier is unnecessary                                                                         |                    | :wrench: | :thought_balloon: |
 | [`@typescript-eslint/no-unnecessary-type-arguments`](./docs/rules/no-unnecessary-type-arguments.md)                   | Enforces that type arguments will not be used if not required                                                           |                    | :wrench: | :thought_balloon: |
 | [`@typescript-eslint/no-unnecessary-type-assertion`](./docs/rules/no-unnecessary-type-assertion.md)                   | Warns if a type assertion does not change the type of an expression                                                     | :heavy_check_mark: | :wrench: | :thought_balloon: |
+| [`@typescript-eslint/no-unsafe-member-access`](./docs/rules/no-unsafe-member-access.md)                               | Disallows member access on any typed variables                                                                          |                    |          | :thought_balloon: |
 | [`@typescript-eslint/no-unused-vars-experimental`](./docs/rules/no-unused-vars-experimental.md)                       | Disallow unused variables and arguments                                                                                 |                    |          | :thought_balloon: |
 | [`@typescript-eslint/no-var-requires`](./docs/rules/no-var-requires.md)                                               | Disallows the use of require statements except in import statements                                                     | :heavy_check_mark: |          |                   |
 | [`@typescript-eslint/prefer-as-const`](./docs/rules/prefer-as-const.md)                                               | Prefer usage of `as const` over literal type                                                                            |                    | :wrench: |                   |
diff --git a/packages/eslint-plugin/ROADMAP.md b/packages/eslint-plugin/ROADMAP.md
index 3c7b5b4edc66..32eb363609c6 100644
--- a/packages/eslint-plugin/ROADMAP.md
+++ b/packages/eslint-plugin/ROADMAP.md
@@ -90,7 +90,7 @@ It lists all TSLint rules along side rules from the ESLint ecosystem that are th
 | [`no-this-assignment`]               | ✅  | [`@typescript-eslint/no-this-alias`]                                                                 |
 | [`no-unbound-method`]                | ✅  | [`@typescript-eslint/unbound-method`]                                                                |
 | [`no-unnecessary-class`]             | ✅  | [`@typescript-eslint/no-extraneous-class`]                                                           |
-| [`no-unsafe-any`]                    | 🛑  | N/A                                                                                                  |
+| [`no-unsafe-any`]                    | 🌓  | [`@typescript-eslint/no-unsafe-member-access`]<sup>[2]</sup>                                         |
 | [`no-unsafe-finally`]                | 🌟  | [`no-unsafe-finally`][no-unsafe-finally]                                                             |
 | [`no-unused-expression`]             | 🌟  | [`no-unused-expressions`][no-unused-expressions]                                                     |
 | [`no-unused-variable`]               | 🌓  | [`@typescript-eslint/no-unused-vars`]                                                                |
@@ -113,6 +113,7 @@ It lists all TSLint rules along side rules from the ESLint ecosystem that are th
 | [`use-isnan`]                        | 🌟  | [`use-isnan`][use-isnan]                                                                             |
 
 <sup>[1]</sup> The ESLint rule also supports silencing with an extra set of parentheses (`if ((foo = bar)) {}`)<br>
+<sup>[2]</sup> Only checks member expressions
 
 ### Maintainability
 
@@ -136,7 +137,6 @@ It lists all TSLint rules along side rules from the ESLint ecosystem that are th
 | [`prefer-readonly`]          | ✅  | [`@typescript-eslint/prefer-readonly`]             |
 | [`trailing-comma`]           | 🌓  | [`comma-dangle`][comma-dangle] or [Prettier]       |
 
-<sup>[1]</sup> Only warns when importing deprecated symbols<br>
 <sup>[2]</sup> Missing support for blank-line-delimited sections
 
 ### Style
@@ -174,7 +174,7 @@ It lists all TSLint rules along side rules from the ESLint ecosystem that are th
 | [`no-reference-import`]             | ✅  | [`@typescript-eslint/triple-slash-reference`]                                       |
 | [`no-trailing-whitespace`]          | 🌟  | [`no-trailing-spaces`][no-trailing-spaces]                                          |
 | [`no-unnecessary-callback-wrapper`] | 🛑  | N/A and this might be unsafe (i.e. with `forEach`)                                  |
-| [`no-unnecessary-else`]             | 🌟  | [`no-else-return`][no-else-return] <sup>[2]</sup                                    |
+| [`no-unnecessary-else`]             | 🌟  | [`no-else-return`][no-else-return] <sup>[2]</sup>                                   |
 | [`no-unnecessary-initializer`]      | 🌟  | [`no-undef-init`][no-undef-init]                                                    |
 | [`no-unnecessary-qualifier`]        | ✅  | [`@typescript-eslint/no-unnecessary-qualifier`]                                     |
 | [`number-literal-format`]           | 🛑  | N/A                                                                                 |
@@ -640,6 +640,7 @@ Relevant plugins: [`chai-expect-keywords`](https://github.com/gavinaiken/eslint-
 [`@typescript-eslint/semi`]: https://github.com/typescript-eslint/typescript-eslint/blob/master/packages/eslint-plugin/docs/rules/semi.md
 [`@typescript-eslint/no-floating-promises`]: https://github.com/typescript-eslint/typescript-eslint/blob/master/packages/eslint-plugin/docs/rules/no-floating-promises.md
 [`@typescript-eslint/no-magic-numbers`]: https://github.com/typescript-eslint/typescript-eslint/blob/master/packages/eslint-plugin/docs/rules/no-magic-numbers.md
+[`@typescript-eslint/no-unsafe-member-access`]: https://github.com/typescript-eslint/typescript-eslint/blob/master/packages/eslint-plugin/docs/rules/no-unsafe-member-access.md
 
 <!-- eslint-plugin-import -->
 
diff --git a/packages/eslint-plugin/docs/rules/no-unsafe-member-access.md b/packages/eslint-plugin/docs/rules/no-unsafe-member-access.md
new file mode 100644
index 000000000000..e99b2536c16e
--- /dev/null
+++ b/packages/eslint-plugin/docs/rules/no-unsafe-member-access.md
@@ -0,0 +1,43 @@
+# Disallows member access on any typed variables (`no-unsafe-member-access`)
+
+Despite your best intentions, the `any` type can sometimes leak into your codebase.
+Member access on `any` typed variables is not checked at all by TypeScript, so it creates a potential safety hole, and source of bugs in your codebase.
+
+## Rule Details
+
+This rule disallows member access on any variable that is typed as `any`.
+
+Examples of **incorrect** code for this rule:
+
+```ts
+declare const anyVar: any;
+declare const nestedAny: { prop: any };
+
+anyVar.a;
+anyVar.a.b;
+anyVar['a'];
+anyVar['a']['b'];
+
+nestedAny.prop.a;
+nestedAny.prop['a'];
+
+const key = 'a';
+nestedAny.prop[key];
+```
+
+Examples of **correct** code for this rule:
+
+```ts
+declare const properlyTyped: { prop: { a: string } };
+
+nestedAny.prop.a;
+nestedAny.prop['a'];
+
+const key = 'a';
+nestedAny.prop[key];
+```
+
+## Related to
+
+- [`no-explicit-any`](./no-explicit-any.md)
+- TSLint: [`no-unsafe-any`](https://palantir.github.io/tslint/rules/no-unsafe-any/)
diff --git a/packages/eslint-plugin/src/configs/all.json b/packages/eslint-plugin/src/configs/all.json
index 590ef81df8d5..47f4e509068a 100644
--- a/packages/eslint-plugin/src/configs/all.json
+++ b/packages/eslint-plugin/src/configs/all.json
@@ -61,6 +61,7 @@
     "@typescript-eslint/no-unnecessary-qualifier": "error",
     "@typescript-eslint/no-unnecessary-type-arguments": "error",
     "@typescript-eslint/no-unnecessary-type-assertion": "error",
+    "@typescript-eslint/no-unsafe-member-access": "error",
     "no-unused-expressions": "off",
     "@typescript-eslint/no-unused-expressions": "error",
     "no-unused-vars": "off",
diff --git a/packages/eslint-plugin/src/rules/index.ts b/packages/eslint-plugin/src/rules/index.ts
index 3568057787b2..f09033aa2d73 100644
--- a/packages/eslint-plugin/src/rules/index.ts
+++ b/packages/eslint-plugin/src/rules/index.ts
@@ -53,6 +53,7 @@ import noUnnecessaryCondition from './no-unnecessary-condition';
 import noUnnecessaryQualifier from './no-unnecessary-qualifier';
 import noUnnecessaryTypeArguments from './no-unnecessary-type-arguments';
 import noUnnecessaryTypeAssertion from './no-unnecessary-type-assertion';
+import noUnsafeMemberAccess from './no-unsafe-member-access';
 import noUntypedPublicSignature from './no-untyped-public-signature';
 import noUnusedExpressions from './no-unused-expressions';
 import noUnusedVars from './no-unused-vars';
@@ -144,6 +145,7 @@ export default {
   'no-unnecessary-qualifier': noUnnecessaryQualifier,
   'no-unnecessary-type-arguments': noUnnecessaryTypeArguments,
   'no-unnecessary-type-assertion': noUnnecessaryTypeAssertion,
+  'no-unsafe-member-access': noUnsafeMemberAccess,
   'no-untyped-public-signature': noUntypedPublicSignature,
   'no-unused-expressions': noUnusedExpressions,
   'no-unused-vars-experimental': noUnusedVarsExperimental,
diff --git a/packages/eslint-plugin/src/rules/no-unsafe-member-access.ts b/packages/eslint-plugin/src/rules/no-unsafe-member-access.ts
new file mode 100644
index 000000000000..298cd97561e9
--- /dev/null
+++ b/packages/eslint-plugin/src/rules/no-unsafe-member-access.ts
@@ -0,0 +1,74 @@
+import { TSESTree } from '@typescript-eslint/experimental-utils';
+import * as util from '../util';
+
+const enum State {
+  Unsafe = 1,
+  Safe = 2,
+}
+
+export default util.createRule({
+  name: 'no-unsafe-member-access',
+  meta: {
+    type: 'problem',
+    docs: {
+      description: 'Disallows member access on any typed variables',
+      category: 'Possible Errors',
+      recommended: false,
+      requiresTypeChecking: true,
+    },
+    messages: {
+      unsafeMemberExpression:
+        'Unsafe member access {{property}} on an any value',
+    },
+    schema: [],
+  },
+  defaultOptions: [],
+  create(context) {
+    const { program, esTreeNodeToTSNodeMap } = util.getParserServices(context);
+    const checker = program.getTypeChecker();
+    const sourceCode = context.getSourceCode();
+
+    const stateCache = new Map<TSESTree.Node, State>();
+
+    function checkMemberExpression(
+      node: TSESTree.MemberExpression | TSESTree.OptionalMemberExpression,
+    ): State {
+      const cachedState = stateCache.get(node);
+      if (cachedState) {
+        return cachedState;
+      }
+
+      if (util.isMemberOrOptionalMemberExpression(node.object)) {
+        const objectState = checkMemberExpression(node.object);
+        if (objectState === State.Unsafe) {
+          // if the object is unsafe, we know this will be unsafe as well
+          // we don't need to report, as we have already reported on the inner member expr
+          stateCache.set(node, objectState);
+          return objectState;
+        }
+      }
+
+      const tsNode = esTreeNodeToTSNodeMap.get(node.object);
+      const type = checker.getTypeAtLocation(tsNode);
+      const state = util.isTypeAnyType(type) ? State.Unsafe : State.Safe;
+      stateCache.set(node, state);
+
+      if (state === State.Unsafe) {
+        const propertyName = sourceCode.getText(node.property);
+        context.report({
+          node,
+          messageId: 'unsafeMemberExpression',
+          data: {
+            property: node.computed ? `[${propertyName}]` : `.${propertyName}`,
+          },
+        });
+      }
+
+      return state;
+    }
+
+    return {
+      'MemberExpression, OptionalMemberExpression': checkMemberExpression,
+    };
+  },
+});
diff --git a/packages/eslint-plugin/src/util/astUtils.ts b/packages/eslint-plugin/src/util/astUtils.ts
index a92f00eaa168..3dffeb90e01f 100644
--- a/packages/eslint-plugin/src/util/astUtils.ts
+++ b/packages/eslint-plugin/src/util/astUtils.ts
@@ -221,6 +221,15 @@ function isAwaitKeyword(
   return node?.type === AST_TOKEN_TYPES.Identifier && node.value === 'await';
 }
 
+function isMemberOrOptionalMemberExpression(
+  node: TSESTree.Node,
+): node is TSESTree.MemberExpression | TSESTree.OptionalMemberExpression {
+  return (
+    node.type === AST_NODE_TYPES.MemberExpression ||
+    node.type === AST_NODE_TYPES.OptionalMemberExpression
+  );
+}
+
 export {
   isAwaitExpression,
   isAwaitKeyword,
@@ -231,6 +240,7 @@ export {
   isFunctionType,
   isIdentifier,
   isLogicalOrOperator,
+  isMemberOrOptionalMemberExpression,
   isNonNullAssertionPunctuator,
   isNotNonNullAssertionPunctuator,
   isNotOptionalChainPunctuator,
diff --git a/packages/eslint-plugin/src/util/types.ts b/packages/eslint-plugin/src/util/types.ts
index eae3519ea214..f59f3d7c53e5 100644
--- a/packages/eslint-plugin/src/util/types.ts
+++ b/packages/eslint-plugin/src/util/types.ts
@@ -290,3 +290,10 @@ export function getEqualsKind(operator: string): EqualsKind | undefined {
       return undefined;
   }
 }
+
+/**
+ * @returns true if the type is `any`
+ */
+export function isTypeAnyType(type: ts.Type): boolean {
+  return isTypeFlagSet(type, ts.TypeFlags.Any);
+}
diff --git a/packages/eslint-plugin/tests/rules/no-unsafe-member-access.test.ts b/packages/eslint-plugin/tests/rules/no-unsafe-member-access.test.ts
new file mode 100644
index 000000000000..641e0492e5ab
--- /dev/null
+++ b/packages/eslint-plugin/tests/rules/no-unsafe-member-access.test.ts
@@ -0,0 +1,85 @@
+import rule from '../../src/rules/no-unsafe-member-access';
+import {
+  RuleTester,
+  batchedSingleLineTests,
+  getFixturesRootDir,
+} from '../RuleTester';
+
+const ruleTester = new RuleTester({
+  parser: '@typescript-eslint/parser',
+  parserOptions: {
+    project: './tsconfig.json',
+    tsconfigRootDir: getFixturesRootDir(),
+  },
+});
+
+ruleTester.run('no-unsafe-member-access', rule, {
+  valid: [
+    'function foo(x: { a: number }) { x.a }',
+    'function foo(x?: { a: number }) { x?.a }',
+  ],
+  invalid: [
+    ...batchedSingleLineTests({
+      code: `
+function foo(x: any) { x.a }
+function foo(x: any) { x.a.b.c.d.e.f.g }
+function foo(x: { a: any }) { x.a.b.c.d.e.f.g }
+      `,
+      errors: [
+        {
+          messageId: 'unsafeMemberExpression',
+          data: {
+            property: '.a',
+          },
+          line: 2,
+          column: 24,
+          endColumn: 27,
+        },
+        {
+          messageId: 'unsafeMemberExpression',
+          data: {
+            property: '.a',
+          },
+          line: 3,
+          column: 24,
+          endColumn: 27,
+        },
+        {
+          messageId: 'unsafeMemberExpression',
+          data: {
+            property: '.b',
+          },
+          line: 4,
+          column: 31,
+          endColumn: 36,
+        },
+      ],
+    }),
+    ...batchedSingleLineTests({
+      code: `
+function foo(x: any) { x['a'] }
+function foo(x: any) { x['a']['b']['c'] }
+      `,
+      errors: [
+        {
+          messageId: 'unsafeMemberExpression',
+          data: {
+            property: "['a']",
+          },
+          line: 2,
+          column: 24,
+          endColumn: 30,
+        },
+        {
+          messageId: 'unsafeMemberExpression',
+          data: {
+            property: "['a']",
+          },
+          line: 3,
+          column: 24,
+          endColumn: 30,
+        },
+      ],
+    }),
+  ],
+});

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