diff --git a/README.md b/README.md
index ae8aa58b9..515e1e0cd 100644
--- a/README.md
+++ b/README.md
@@ -127,6 +127,7 @@ installations requiring long-term consistency.
 
 | Rule                           | Description                                                       | Configurations   | Fixable             |
 | ------------------------------ | ----------------------------------------------------------------- | ---------------- | ------------------- |
+| [ban-matchers][]               | Bans specific matchers & modifiers from being used                |                  |                     |
 | [consistent-test-it][]         | Enforce consistent test or it keyword                             |                  | ![fixable-green][]  |
 | [expect-expect][]              | Enforce assertion to be made in a test body                       | ![recommended][] |                     |
 | [lowercase-name][]             | Disallow capitalized test names                                   |                  | ![fixable-green][]  |
@@ -183,6 +184,7 @@ ensure consistency and readability in jest test suites.
 
 https://github.com/dangreenisrael/eslint-plugin-jest-formatting
 
+[ban-matchers]: docs/rules/ban-matchers.md
 [consistent-test-it]: docs/rules/consistent-test-it.md
 [expect-expect]: docs/rules/expect-expect.md
 [lowercase-name]: docs/rules/lowercase-name.md
diff --git a/docs/rules/ban-matchers.md b/docs/rules/ban-matchers.md
new file mode 100644
index 000000000..abdc52548
--- /dev/null
+++ b/docs/rules/ban-matchers.md
@@ -0,0 +1,47 @@
+# Bans specific matchers & modifiers from being used (`ban-matchers`)
+
+This rule bans specific matchers & modifiers from being used, and can suggest
+alternatives.
+
+## Rule Details
+
+Bans are expressed in the form of a map, with the value being either a string
+message to be shown, or `null` if the default rule message should be used.
+
+Both matchers, modifiers, and chains of the two are checked, allowing for
+specific variations of a matcher to be banned if desired.
+
+By default, this map is empty, meaning no matchers or modifiers are banned.
+
+For example:
+
+```json
+{
+  "jest/ban-matchers": [
+    "error",
+    {
+      "toBeFalsy": null,
+      "resolves": "Use `expect(await promise)` instead.",
+      "not.toHaveBeenCalledWith": null
+    }
+  ]
+}
+```
+
+Examples of **incorrect** code for this rule with the above configuration
+
+```js
+it('is false', () => {
+  expect(a).toBeFalsy();
+});
+
+it('resolves', async () => {
+  await expect(myPromise()).resolves.toBe(true);
+});
+
+describe('when an error happens', () => {
+  it('does not upload the file', async () => {
+    expect(uploadFileMock).not.toHaveBeenCalledWith('file.name');
+  });
+});
+```
diff --git a/src/__tests__/__snapshots__/rules.test.ts.snap b/src/__tests__/__snapshots__/rules.test.ts.snap
index ec79e907d..207d076a2 100644
--- a/src/__tests__/__snapshots__/rules.test.ts.snap
+++ b/src/__tests__/__snapshots__/rules.test.ts.snap
@@ -10,6 +10,7 @@ Object {
       "jest",
     ],
     "rules": Object {
+      "jest/ban-matchers": "error",
       "jest/consistent-test-it": "error",
       "jest/expect-expect": "error",
       "jest/lowercase-name": "error",
diff --git a/src/__tests__/rules.test.ts b/src/__tests__/rules.test.ts
index eee9d9c32..ec4461e4a 100644
--- a/src/__tests__/rules.test.ts
+++ b/src/__tests__/rules.test.ts
@@ -3,7 +3,7 @@ import { resolve } from 'path';
 import plugin from '../';
 
 const ruleNames = Object.keys(plugin.rules);
-const numberOfRules = 41;
+const numberOfRules = 42;
 
 describe('rules', () => {
   it('should have a corresponding doc for each rule', () => {
diff --git a/src/rules/__tests__/ban-matchers.test.ts b/src/rules/__tests__/ban-matchers.test.ts
new file mode 100644
index 000000000..81c432da3
--- /dev/null
+++ b/src/rules/__tests__/ban-matchers.test.ts
@@ -0,0 +1,185 @@
+import { TSESLint } from '@typescript-eslint/experimental-utils';
+import resolveFrom from 'resolve-from';
+import rule from '../ban-matchers';
+
+const ruleTester = new TSESLint.RuleTester({
+  parser: resolveFrom(require.resolve('eslint'), 'espree'),
+  parserOptions: {
+    ecmaVersion: 2017,
+  },
+});
+
+ruleTester.run('ban-matchers', rule, {
+  valid: [
+    'expect(a).toHaveBeenCalled()',
+    'expect(a).not.toHaveBeenCalled()',
+    'expect(a).toHaveBeenCalledTimes()',
+    'expect(a).toHaveBeenCalledWith()',
+    'expect(a).toHaveBeenLastCalledWith()',
+    'expect(a).toHaveBeenNthCalledWith()',
+    'expect(a).toHaveReturned()',
+    'expect(a).toHaveReturnedTimes()',
+    'expect(a).toHaveReturnedWith()',
+    'expect(a).toHaveLastReturnedWith()',
+    'expect(a).toHaveNthReturnedWith()',
+    'expect(a).toThrow()',
+    'expect(a).rejects;',
+    'expect(a);',
+    {
+      code: 'expect(a).resolves',
+      options: [{ not: null }],
+    },
+    {
+      code: 'expect(a).toBe(b)',
+      options: [{ 'not.toBe': null }],
+    },
+    {
+      code: 'expect(a)["toBe"](b)',
+      options: [{ 'not.toBe': null }],
+    },
+  ],
+  invalid: [
+    {
+      code: 'expect(a).toBe(b)',
+      options: [{ toBe: null }],
+      errors: [
+        {
+          messageId: 'bannedChain',
+          data: {
+            message: null,
+            chain: 'toBe',
+          },
+          column: 11,
+          line: 1,
+        },
+      ],
+    },
+    {
+      code: 'expect(a)["toBe"](b)',
+      options: [{ toBe: null }],
+      errors: [
+        {
+          messageId: 'bannedChain',
+          data: {
+            message: null,
+            chain: 'toBe',
+          },
+          column: 11,
+          line: 1,
+        },
+      ],
+    },
+    {
+      code: 'expect(a).not',
+      options: [{ not: null }],
+      errors: [
+        {
+          messageId: 'bannedChain',
+          data: {
+            message: null,
+            chain: 'not',
+          },
+          column: 11,
+          line: 1,
+        },
+      ],
+    },
+    {
+      code: 'expect(a).not.toBe(b)',
+      options: [{ not: null }],
+      errors: [
+        {
+          messageId: 'bannedChain',
+          data: {
+            message: null,
+            chain: 'not',
+          },
+          column: 11,
+          line: 1,
+        },
+      ],
+    },
+    {
+      code: 'expect(a).not.toBe(b)',
+      options: [{ 'not.toBe': null }],
+      errors: [
+        {
+          messageId: 'bannedChain',
+          data: {
+            message: null,
+            chain: 'not.toBe',
+          },
+          endColumn: 19,
+          column: 11,
+          line: 1,
+        },
+      ],
+    },
+    {
+      code: 'expect(a).toBe(b)',
+      options: [{ toBe: 'Prefer `toStrictEqual` instead' }],
+      errors: [
+        {
+          messageId: 'bannedChainWithMessage',
+          data: {
+            message: 'Prefer `toStrictEqual` instead',
+            chain: 'toBe',
+          },
+          column: 11,
+          line: 1,
+        },
+      ],
+    },
+    {
+      code: `
+        test('some test', async () => {
+          await expect(Promise.resolve(1)).resolves.toBe(1);
+         });
+      `,
+      options: [{ resolves: 'Use `expect(await promise)` instead.' }],
+      errors: [
+        {
+          messageId: 'bannedChainWithMessage',
+          data: {
+            message: 'Use `expect(await promise)` instead.',
+            chain: 'resolves',
+          },
+          endColumn: 52,
+          column: 44,
+        },
+      ],
+    },
+    {
+      code: 'expect(Promise.resolve({})).rejects.toBeFalsy()',
+      options: [{ toBeFalsy: null }],
+      errors: [
+        {
+          messageId: 'bannedChain',
+          data: {
+            message: null,
+            chain: 'toBeFalsy',
+          },
+          endColumn: 46,
+          column: 37,
+        },
+      ],
+    },
+    {
+      code: "expect(uploadFileMock).not.toHaveBeenCalledWith('file.name')",
+      options: [
+        { 'not.toHaveBeenCalledWith': 'Use not.toHaveBeenCalled instead' },
+      ],
+      errors: [
+        {
+          messageId: 'bannedChainWithMessage',
+          data: {
+            message: 'Use not.toHaveBeenCalled instead',
+            chain: 'not.toHaveBeenCalledWith',
+          },
+          endColumn: 48,
+          column: 24,
+        },
+      ],
+    },
+  ],
+});
diff --git a/src/rules/ban-matchers.ts b/src/rules/ban-matchers.ts
new file mode 100644
index 000000000..57585f8d6
--- /dev/null
+++ b/src/rules/ban-matchers.ts
@@ -0,0 +1,91 @@
+import { createRule, isExpectCall, parseExpectCall } from './utils';
+
+export default createRule<
+  [Record<string, string | null>],
+  'bannedChain' | 'bannedChainWithMessage'
+>({
+  name: __filename,
+  meta: {
+    docs: {
+      category: 'Best Practices',
+      description: 'Bans specific matchers & modifiers from being used',
+      recommended: false,
+    },
+    type: 'suggestion',
+    schema: [
+      {
+        type: 'object',
+        additionalProperties: {
+          type: ['string', 'null'],
+        },
+      },
+    ],
+    messages: {
+      bannedChain: '{{ chain }} is banned, and so should not be used',
+      bannedChainWithMessage: '{{ message }}',
+    },
+  },
+  defaultOptions: [{}],
+  create(context, [bannedChains]) {
+    return {
+      CallExpression(node) {
+        if (!isExpectCall(node)) {
+          return;
+        }
+
+        const { matcher, modifier } = parseExpectCall(node);
+
+        if (matcher) {
+          const chain = matcher.name;
+
+          if (chain in bannedChains) {
+            const message = bannedChains[chain];
+
+            context.report({
+              messageId: message ? 'bannedChainWithMessage' : 'bannedChain',
+              data: { message, chain },
+              node: matcher.node.property,
+            });
+
+            return;
+          }
+        }
+
+        if (modifier) {
+          const chain = modifier.name;
+
+          if (chain in bannedChains) {
+            const message = bannedChains[chain];
+
+            context.report({
+              messageId: message ? 'bannedChainWithMessage' : 'bannedChain',
+              data: { message, chain },
+              node: modifier.node.property,
+            });
+
+            return;
+          }
+        }
+
+        if (matcher && modifier) {
+          const chain = `${modifier.name}.${matcher.name}`;
+
+          if (chain in bannedChains) {
+            const message = bannedChains[chain];
+
+            context.report({
+              messageId: message ? 'bannedChainWithMessage' : 'bannedChain',
+              data: { message, chain },
+              loc: {
+                start: modifier.node.property.loc.start,
+                end: matcher.node.property.loc.end,
+              },
+            });
+
+            return;
+          }
+        }
+      },
+    };
+  },
+});