diff --git a/tornado/netutil.py b/tornado/netutil.py
index e83afad570..b0cf21c5a3 100644
--- a/tornado/netutil.py
+++ b/tornado/netutil.py
@@ -209,17 +209,20 @@ def bind_unix_socket(
                 # Hurd doesn't support SO_REUSEADDR
                 raise
         sock.setblocking(False)
-        try:
-            st = os.stat(file)
-        except FileNotFoundError:
-            pass
-        else:
-            if stat.S_ISSOCK(st.st_mode):
-                os.remove(file)
+        if not file.startswith("\0"):
+            try:
+                st = os.stat(file)
+            except FileNotFoundError:
+                pass
             else:
-                raise ValueError("File %s exists and is not a socket", file)
-        sock.bind(file)
-        os.chmod(file, mode)
+                if stat.S_ISSOCK(st.st_mode):
+                    os.remove(file)
+                else:
+                    raise ValueError("File %s exists and is not a socket", file)
+            sock.bind(file)
+            os.chmod(file, mode)
+        else:
+            sock.bind(file)
         sock.listen(backlog)
         return sock
 
diff --git a/tornado/test/httpserver_test.py b/tornado/test/httpserver_test.py
index 762c23f6e0..2d16cf2f0c 100644
--- a/tornado/test/httpserver_test.py
+++ b/tornado/test/httpserver_test.py
@@ -834,15 +834,14 @@ def setUp(self):
         super().setUp()
         self.tmpdir = tempfile.mkdtemp()
         self.sockfile = os.path.join(self.tmpdir, "test.sock")
-        sock = netutil.bind_unix_socket(self.sockfile)
         app = Application([("/hello", HelloWorldRequestHandler)])
         self.server = HTTPServer(app)
-        self.server.add_socket(sock)
-        self.stream = IOStream(socket.socket(socket.AF_UNIX))
-        self.io_loop.run_sync(lambda: self.stream.connect(self.sockfile))
+        if sys.platform.startswith('linux'):
+            self.sockabstract = "\0" + os.path.basename(self.tmpdir)
+            self.server.add_socket(netutil.bind_unix_socket(self.sockabstract))
+        self.server.add_socket(netutil.bind_unix_socket(self.sockfile))
 
     def tearDown(self):
-        self.stream.close()
         self.io_loop.run_sync(self.server.close_all_connections)
         self.server.stop()
         shutil.rmtree(self.tmpdir)
@@ -850,21 +849,38 @@ def tearDown(self):
 
     @gen_test
     def test_unix_socket(self):
-        self.stream.write(b"GET /hello HTTP/1.0\r\n\r\n")
-        response = yield self.stream.read_until(b"\r\n")
-        self.assertEqual(response, b"HTTP/1.1 200 OK\r\n")
-        header_data = yield self.stream.read_until(b"\r\n\r\n")
-        headers = HTTPHeaders.parse(header_data.decode("latin1"))
-        body = yield self.stream.read_bytes(int(headers["Content-Length"]))
-        self.assertEqual(body, b"Hello world")
+        with closing(IOStream(socket.socket(socket.AF_UNIX))) as stream:
+            stream.connect(self.sockfile)
+            stream.write(b"GET /hello HTTP/1.0\r\n\r\n")
+            response = yield stream.read_until(b"\r\n")
+            self.assertEqual(response, b"HTTP/1.1 200 OK\r\n")
+            header_data = yield stream.read_until(b"\r\n\r\n")
+            headers = HTTPHeaders.parse(header_data.decode("latin1"))
+            body = yield stream.read_bytes(int(headers["Content-Length"]))
+            self.assertEqual(body, b"Hello world")
+
+    @unittest.skipUnless(sys.platform.startswith('linux'), 'requires Linux')
+    @gen_test
+    def test_unix_socket_abstract(self):
+        with closing(IOStream(socket.socket(socket.AF_UNIX))) as stream:
+            stream.connect(self.sockabstract)
+            stream.write(b"GET /hello HTTP/1.0\r\n\r\n")
+            response = yield stream.read_until(b"\r\n")
+            self.assertEqual(response, b"HTTP/1.1 200 OK\r\n")
+            header_data = yield stream.read_until(b"\r\n\r\n")
+            headers = HTTPHeaders.parse(header_data.decode("latin1"))
+            body = yield stream.read_bytes(int(headers["Content-Length"]))
+            self.assertEqual(body, b"Hello world")
 
     @gen_test
     def test_unix_socket_bad_request(self):
         # Unix sockets don't have remote addresses so they just return an
         # empty string.
         with ExpectLog(gen_log, "Malformed HTTP message from", level=logging.INFO):
-            self.stream.write(b"garbage\r\n\r\n")
-            response = yield self.stream.read_until_close()
+            with closing(IOStream(socket.socket(socket.AF_UNIX))) as stream:
+                stream.connect(self.sockfile)
+                stream.write(b"garbage\r\n\r\n")
+                response = yield stream.read_until_close()
         self.assertEqual(response, b"HTTP/1.1 400 Bad Request\r\n\r\n")