diff --git a/packages/terser/README.md b/packages/terser/README.md
index b9f765f82..1cf4f8382 100644
--- a/packages/terser/README.md
+++ b/packages/terser/README.md
@@ -73,6 +73,8 @@ export default {
 };
 ```
 
+Note: when a [`nameCache`](https://github.com/terser/terser#minify-options) is provided, chunks are minified sequentially on a single worker regardless of `maxWorkers`, since a shared name cache requires sequential minification to mangle names consistently across chunks.
+
 ## Meta
 
 [CONTRIBUTING](/.github/CONTRIBUTING.md)
diff --git a/packages/terser/src/module.ts b/packages/terser/src/module.ts
index 2877a6e49..cea533a41 100644
--- a/packages/terser/src/module.ts
+++ b/packages/terser/src/module.ts
@@ -13,6 +13,10 @@ export default function terser(input: Options = {}) {
   let numOfChunks = 0;
   let numOfWorkersUsed = 0;
 
+  // Chained minify tasks; used only when a shared nameCache is provided,
+  // since terser requires sequential minification for consistent mangling.
+  let nameCacheChain: Promise<unknown> = Promise.resolve();
+
   return {
     name: 'terser',
 
@@ -24,6 +28,8 @@ export default function terser(input: Options = {}) {
         });
       }
 
+      const pool = workerPool;
+
       numOfChunks += 1;
 
       const defaultOptions: Options = {
@@ -38,12 +44,12 @@ export default function terser(input: Options = {}) {
         defaultOptions.toplevel = true;
       }
 
-      try {
+      const runTask = async () => {
         const {
           code: result,
           nameCache,
           sourceMap
-        } = await workerPool.addAsync({
+        } = await pool.addAsync({
           code,
           options: merge({}, options || {}, defaultOptions)
         });
@@ -79,13 +85,28 @@ export default function terser(input: Options = {}) {
           options.nameCache.props = props;
         }
 
-        if ((!!defaultOptions.sourceMap || !!options.sourceMap) && isObject(sourceMap)) {
+        return { result, sourceMap };
+      };
+
+      try {
+        let output;
+        if (options.nameCache) {
+          // The options snapshot and its serialization must only happen once
+          // the previous chunk's nameCache has been merged back.
+          const task = nameCacheChain.then(runTask);
+          nameCacheChain = task.catch(() => {});
+          output = await task;
+        } else {
+          output = await runTask();
+        }
+
+        if ((!!defaultOptions.sourceMap || !!options.sourceMap) && isObject(output.sourceMap)) {
           return {
-            code: result,
-            map: sourceMap
+            code: output.result,
+            map: output.sourceMap
           };
         }
-        return result;
+        return output.result;
       } catch (e) {
         return Promise.reject(e);
       } finally {
diff --git a/packages/terser/test/fixtures/chunk-1.js b/packages/terser/test/fixtures/chunk-1.js
index daff3a741..c27eb3d83 100644
--- a/packages/terser/test/fixtures/chunk-1.js
+++ b/packages/terser/test/fixtures/chunk-1.js
@@ -1,2 +1 @@
-const chunk1 = 'chunk-1';
-console.log(chunk1)
+console.log({ _name: 'chunk-1', _size: 1 });
diff --git a/packages/terser/test/fixtures/chunk-2.js b/packages/terser/test/fixtures/chunk-2.js
index 7c4513c6e..8db5e9338 100644
--- a/packages/terser/test/fixtures/chunk-2.js
+++ b/packages/terser/test/fixtures/chunk-2.js
@@ -1,2 +1 @@
-const chunk2 = 'chunk-2';
-console.log(chunk2)
+console.log({ _size: 2, _name: 'chunk-2' });
diff --git a/packages/terser/test/fixtures/name-cache-entry-1.js b/packages/terser/test/fixtures/name-cache-entry-1.js
new file mode 100644
index 000000000..013f534ef
--- /dev/null
+++ b/packages/terser/test/fixtures/name-cache-entry-1.js
@@ -0,0 +1,4 @@
+/* eslint-disable no-underscore-dangle */
+import { Foo } from './name-cache-shared.js';
+
+console.log(new Foo()._bar());
diff --git a/packages/terser/test/fixtures/name-cache-entry-2.js b/packages/terser/test/fixtures/name-cache-entry-2.js
new file mode 100644
index 000000000..4c7e5b72f
--- /dev/null
+++ b/packages/terser/test/fixtures/name-cache-entry-2.js
@@ -0,0 +1,4 @@
+/* eslint-disable no-underscore-dangle */
+import { Foo } from './name-cache-shared.js';
+
+console.log(new Foo()._baz(), new Foo()._bar());
diff --git a/packages/terser/test/fixtures/name-cache-shared.js b/packages/terser/test/fixtures/name-cache-shared.js
new file mode 100644
index 000000000..0d7198c87
--- /dev/null
+++ b/packages/terser/test/fixtures/name-cache-shared.js
@@ -0,0 +1,9 @@
+/* eslint-disable class-methods-use-this, no-underscore-dangle */
+export class Foo {
+  _bar() {
+    return 'bar';
+  }
+  _baz() {
+    return 'baz';
+  }
+}
diff --git a/packages/terser/test/test.js b/packages/terser/test/test.js
index 78366dbc3..447ac9c16 100644
--- a/packages/terser/test/test.js
+++ b/packages/terser/test/test.js
@@ -432,3 +432,144 @@ test.sequential('terser preserve vars in nameCache when provided', async () => {
     }
   });
 });
+
+// https://github.com/rollup/plugins/issues/1970
+// The same property must mangle to the same name in every chunk of a build.
+async function buildSharedImportChunks(maxWorkers) {
+  const nameCache = {};
+  const bundle = await rollup({
+    input: ['test/fixtures/name-cache-entry-1.js', 'test/fixtures/name-cache-entry-2.js'],
+    plugins: [
+      terser({
+        mangle: {
+          properties: {
+            regex: /^_/
+          }
+        },
+        nameCache,
+        maxWorkers
+      })
+    ]
+  });
+  const result = await bundle.generate({
+    format: 'es',
+    chunkFileNames: 'chunk-[name].js'
+  });
+  expect(result.output.length).toBe(3);
+  const bar = nameCache.props.props.$_bar;
+  const baz = nameCache.props.props.$_baz;
+  expect(bar).toBeTruthy();
+  expect(baz).toBeTruthy();
+  expect(bar).not.toBe(baz);
+  for (const chunk of result.output) {
+    expect(chunk.code).not.toContain('_bar');
+    expect(chunk.code).not.toContain('_baz');
+  }
+  const entry1 = result.output.find((chunk) => chunk.fileName === 'name-cache-entry-1.js');
+  const entry2 = result.output.find((chunk) => chunk.fileName === 'name-cache-entry-2.js');
+  const shared = result.output.find((chunk) => !chunk.isEntry);
+  expect(entry1.code).toContain(`.${bar}(`);
+  expect(entry2.code).toContain(`.${bar}(`);
+  expect(entry2.code).toContain(`.${baz}(`);
+  expect(shared.code).toContain(`${bar}(){return"bar"}`);
+  expect(shared.code).toContain(`${baz}(){return"baz"}`);
+}
+test.sequential('shares nameCache between chunks with a common import', async () => {
+  await buildSharedImportChunks();
+});
+test.sequential(
+  'shares nameCache between chunks with a common import with only 1 worker',
+  async () => {
+    await buildSharedImportChunks(1);
+  }
+);
+
+async function buildUnrelatedChunks(maxWorkers) {
+  const nameCache = {};
+  const bundle = await rollup({
+    input: ['test/fixtures/chunk-1.js', 'test/fixtures/chunk-2.js'],
+    plugins: [
+      terser({
+        mangle: {
+          properties: {
+            regex: /^_/
+          }
+        },
+        nameCache,
+        maxWorkers
+      })
+    ]
+  });
+  const result = await bundle.generate({
+    format: 'es'
+  });
+  expect(result.output.length).toBe(2);
+  const name = nameCache.props.props.$_name;
+  const size = nameCache.props.props.$_size;
+  expect(name).toBeTruthy();
+  expect(size).toBeTruthy();
+  expect(name).not.toBe(size);
+  const chunk1 = result.output.find((chunk) => chunk.fileName === 'chunk-1.js');
+  const chunk2 = result.output.find((chunk) => chunk.fileName === 'chunk-2.js');
+  expect(chunk1.code).toContain(`${name}:"chunk-1"`);
+  expect(chunk1.code).toContain(`${size}:1`);
+  expect(chunk2.code).toContain(`${name}:"chunk-2"`);
+  expect(chunk2.code).toContain(`${size}:2`);
+}
+test.sequential('shares nameCache between unrelated chunks', async () => {
+  await buildUnrelatedChunks();
+});
+test.sequential('shares nameCache between unrelated chunks with only 1 worker', async () => {
+  await buildUnrelatedChunks(1);
+});
+
+test.sequential('mangles unrelated chunks independently without a nameCache', async () => {
+  const bundle = await rollup({
+    input: ['test/fixtures/chunk-1.js', 'test/fixtures/chunk-2.js'],
+    plugins: [
+      terser({
+        mangle: {
+          properties: {
+            regex: /^_/
+          }
+        }
+      })
+    ]
+  });
+  const result = await bundle.generate({
+    format: 'es'
+  });
+  expect(result.output.length).toBe(2);
+  const chunk1 = result.output.find((chunk) => chunk.fileName === 'chunk-1.js');
+  const chunk2 = result.output.find((chunk) => chunk.fileName === 'chunk-2.js');
+  const [, chunk1Name] = chunk1.code.match(/[{,]([$\w]+):"chunk-1"/);
+  const [, chunk2Name] = chunk2.code.match(/[{,]([$\w]+):"chunk-2"/);
+  expect(chunk1Name).toBeTruthy();
+  expect(chunk2Name).toBeTruthy();
+  // Each chunk starts from its own empty cache, so the first `_`-property
+  // encountered in each file gets the same first mangled name; `_name` is
+  // declared first in chunk-1 and second in chunk-2, so its name diverges.
+  expect(chunk1Name).not.toBe(chunk2Name);
+});
+
+test.sequential('uses a single worker when a nameCache is shared', async () => {
+  let plugin;
+  const bundle = await rollup({
+    input: ['test/fixtures/name-cache-entry-1.js', 'test/fixtures/name-cache-entry-2.js'],
+    plugins: [
+      (plugin = terser({
+        mangle: {
+          properties: {
+            regex: /^_/
+          }
+        },
+        nameCache: {},
+        maxWorkers: 4
+      }))
+    ]
+  });
+  await bundle.generate({
+    format: 'es'
+  });
+  expect(plugin.numOfWorkersUsed).toBe(1);
+});