diff --git a/spec-dtslint/observables/dom/fetch-spec.ts b/spec-dtslint/observables/dom/fetch-spec.ts
new file mode 100644
index 0000000000..ac155b544c
--- /dev/null
+++ b/spec-dtslint/observables/dom/fetch-spec.ts
@@ -0,0 +1,18 @@
+import { fromFetch } from 'rxjs/fetch';
+import { a$ } from '../../helpers';
+
+it('should emit the fetch Response by default', () => {
+  const a = fromFetch("a"); // $ExpectType Observable<Response>
+});
+
+it('should support a selector that returns a Response promise', () => {
+  const a = fromFetch("a", { selector: response => response.text() }); // $ExpectType Observable<string>
+});
+
+it('should support a selector that returns an arbitrary type', () => {
+  const a = fromFetch("a", { selector: response => a$ }); // $ExpectType Observable<A>
+});
+
+it('should error for selectors that don\'t return an ObservableInput', () => {
+  const a = fromFetch("a", { selector: response => 42 }); // $ExpectError
+});
diff --git a/spec-dtslint/tsconfig.json b/spec-dtslint/tsconfig.json
index 6339f6dd64..86e857a69b 100644
--- a/spec-dtslint/tsconfig.json
+++ b/spec-dtslint/tsconfig.json
@@ -6,7 +6,11 @@
     "noEmit": true,
     "paths": {
       "rxjs": ["../dist/types"],
-      "rxjs/operators": ["../dist/types/operators"]
+      "rxjs/ajax": ["../dist/types/ajax"],
+      "rxjs/fetch": ["../dist/types/fetch"],
+      "rxjs/operators": ["../dist/types/operators"],
+      "rxjs/testing": ["../dist/types/testing"],
+      "rxjs/webSocket": ["../dist/types/webSocket"]
     },
     "skipLibCheck": true,
     "strict": true,
diff --git a/spec/observables/dom/fetch-spec.ts b/spec/observables/dom/fetch-spec.ts
index ce914e6942..81e111e0f9 100644
--- a/spec/observables/dom/fetch-spec.ts
+++ b/spec/observables/dom/fetch-spec.ts
@@ -264,4 +264,57 @@ describe('fromFetch', () => {
       }
     });
   });
+
+  it('should support a selector', done => {
+    mockFetch.respondWith = {
+      ...OK_RESPONSE,
+      text: () => Promise.resolve('bar')
+    };
+    const fetch$ = fromFetch('/foo', {
+      selector: response => response.text()
+    });
+    expect(mockFetch.calls.length).to.equal(0);
+    expect(MockAbortController.created).to.equal(0);
+
+    fetch$.subscribe({
+      next: text => {
+        expect(text).to.equal('bar');
+      },
+      error: done,
+      complete: () => {
+        // Wait until the complete and the subsequent unsubscribe are finished
+        // before testing these expectations:
+        setTimeout(() => {
+          expect(MockAbortController.created).to.equal(1);
+          expect(mockFetch.calls.length).to.equal(1);
+          expect(mockFetch.calls[0].input).to.equal('/foo');
+          expect(mockFetch.calls[0].init!.signal).not.to.be.undefined;
+          expect(mockFetch.calls[0].init!.signal!.aborted).to.be.false;
+          done();
+        }, 0);
+      }
+    });
+  });
+
+  it('should abort when unsubscribed and a selector is specified', () => {
+    mockFetch.respondWith = {
+      ...OK_RESPONSE,
+      text: () => Promise.resolve('bar')
+    };
+    const fetch$ = fromFetch('/foo', {
+      selector: response => response.text()
+    });
+    expect(mockFetch.calls.length).to.equal(0);
+    expect(MockAbortController.created).to.equal(0);
+    const subscription = fetch$.subscribe();
+
+    expect(MockAbortController.created).to.equal(1);
+    expect(mockFetch.calls.length).to.equal(1);
+    expect(mockFetch.calls[0].input).to.equal('/foo');
+    expect(mockFetch.calls[0].init!.signal).not.to.be.undefined;
+    expect(mockFetch.calls[0].init!.signal!.aborted).to.be.false;
+
+    subscription.unsubscribe();
+    expect(mockFetch.calls[0].init!.signal!.aborted).to.be.true;
+  });
 });
diff --git a/src/internal/observable/dom/fetch.ts b/src/internal/observable/dom/fetch.ts
index 0a7e6ab2b6..5ff824bfea 100644
--- a/src/internal/observable/dom/fetch.ts
+++ b/src/internal/observable/dom/fetch.ts
@@ -1,5 +1,19 @@
 import { Observable } from '../../Observable';
 import { Subscription } from '../../Subscription';
+import { from } from '../../observable/from';
+import { ObservableInput } from '../../types';
+
+export function fromFetch<T>(
+  input: string | Request,
+  init: RequestInit & {
+    selector: (response: Response) => ObservableInput<T>
+  }
+): Observable<T>;
+
+export function fromFetch(
+  input: string | Request,
+  init?: RequestInit
+): Observable<Response>;
 
 /**
  * Uses [the Fetch API](https://developer.mozilla.org/en-US/docs/Web/API/Fetch_API) to
@@ -42,7 +56,36 @@ import { Subscription } from '../../Subscription';
  * data$.subscribe({
  *  next: result => console.log(result),
  *  complete: () => console.log('done')
- * })
+ * });
+ * ```
+ *
+ * ### Use with Chunked Transfer Encoding
+ *
+ * With HTTP responses that use [chunked transfer encoding](https://tools.ietf.org/html/rfc7230#section-3.3.1),
+ * the promise returned by `fetch` will resolve as soon as the response's headers are
+ * received.
+ *
+ * That means the `fromFetch` observable will emit a `Response` - and will
+ * then complete - before the body is received. When one of the methods on the
+ * `Response` - like `text()` or `json()` - is called, the returned promise will not
+ * resolve until the entire body has been received. Unsubscribing from any observable
+ * that uses the promise as an observable input will not abort the request.
+ *
+ * To facilitate aborting the retrieval of responses that use chunked transfer encoding,
+ * a `selector` can be specified via the `init` parameter:
+ *
+ * ```ts
+ * import { of } from 'rxjs';
+ * import { fromFetch } from 'rxjs/fetch';
+ *
+ * const data$ = fromFetch('https://api.github.com/users?per_page=5', {
+ *   selector: response => response.json()
+ * });
+ *
+ * data$.subscribe({
+ *  next: result => console.log(result),
+ *  complete: () => console.log('done')
+ * });
  * ```
  *
  * @param input The resource you would like to fetch. Can be a url or a request object.
@@ -51,8 +94,14 @@ import { Subscription } from '../../Subscription';
  * @returns An Observable, that when subscribed to performs an HTTP request using the native `fetch`
  * function. The {@link Subscription} is tied to an `AbortController` for the the fetch.
  */
-export function fromFetch(input: string | Request, init?: RequestInit): Observable<Response> {
-  return new Observable<Response>(subscriber => {
+export function fromFetch<T>(
+  input: string | Request,
+  initWithSelector: RequestInit & {
+    selector?: (response: Response) => ObservableInput<T>
+  } = {}
+): Observable<Response | T> {
+  const { selector, ...init } = initWithSelector;
+  return new Observable<Response | T>(subscriber => {
     const controller = new AbortController();
     const signal = controller.signal;
     let abortable = true;
@@ -91,9 +140,26 @@ export function fromFetch(input: string | Request, init?: RequestInit): Observab
     }
 
     fetch(input, perSubscriberInit).then(response => {
-      abortable = false;
-      subscriber.next(response);
-      subscriber.complete();
+      if (selector) {
+        subscription.add(from(selector(response)).subscribe(
+          value => subscriber.next(value),
+          err => {
+            abortable = false;
+            if (!unsubscribed) {
+              // Only forward the error if it wasn't an abort.
+              subscriber.error(err);
+            }
+          },
+          () => {
+            abortable = false;
+            subscriber.complete();
+          }
+        ));
+      } else {
+        abortable = false;
+        subscriber.next(response);
+        subscriber.complete();
+      }
     }).catch(err => {
       abortable = false;
       if (!unsubscribed) {