diff --git a/Lib/test/test_multiprocessing.py b/Lib/test/test_multiprocessing.py
index 18066ba..d3620b7 100644
--- a/Lib/test/test_multiprocessing.py
+++ b/Lib/test/test_multiprocessing.py
@@ -1213,8 +1213,9 @@
 
     def test_rapid_restart(self):
         authkey = os.urandom(32)
+        port = test.support.find_unused_port()
         manager = QueueManager(
-            address=('localhost', 9999), authkey=authkey, serializer=SERIALIZER)
+            address=('localhost', port), authkey=authkey, serializer=SERIALIZER)
         manager.start()
 
         p = self.Process(target=self._putter, args=(manager.address, authkey))
@@ -1224,7 +1225,7 @@
         del queue
         manager.shutdown()
         manager = QueueManager(
-            address=('localhost', 9999), authkey=authkey, serializer=SERIALIZER)
+            address=('localhost', port), authkey=authkey, serializer=SERIALIZER)
         manager.start()
         manager.shutdown()
 
diff --git a/Misc/NEWS b/Misc/NEWS
index 4b5d102..7ed716c 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -214,6 +214,9 @@
 Tests
 -----
 
+- Issue #7498: test_multiprocessing now uses test.support.find_unused_port
+  instead of a hardcoded port number in test_rapid_restart.
+
 - Issue #7431: use TESTFN in test_linecache instead of trying to create a 
   file in the Lib/test directory, which might be read-only for the
   user running the tests.