diff -r 1940b72b0a02 Lib/test/support/__init__.py
--- a/Lib/test/support/__init__.py	Tue Nov 08 20:34:22 2016 +0200
+++ b/Lib/test/support/__init__.py	Fri Nov 11 16:31:53 2016 +0100
@@ -90,7 +90,7 @@
     "bigmemtest", "bigaddrspacetest", "cpython_only", "get_attribute",
     "requires_IEEE_754", "skip_unless_xattr", "requires_zlib",
     "anticipate_failure", "load_package_tests", "detect_api_mismatch",
-    "check__all__",
+    "check__all__", "requires_multiprocessing_queue",
     # sys
     "is_jython", "is_android", "check_impl_detail", "unix_shell",
     # network
@@ -1744,6 +1744,24 @@
         msg = msg.format(' or '.join(guardnames))
     return unittest.skip(msg)
 
+_have_mp_queue = None
+def requires_multiprocessing_queue():
+    global _have_mp_queue
+    if _have_mp_queue is None:
+        import multiprocessing
+        # Without a functioning shared semaphore implementation attempts to
+        # instantiate a Queue will result in an ImportError (issue #3770).
+        try:
+            multiprocessing.Queue()
+            _have_mp_queue = True
+        except ImportError:
+            _have_mp_queue = False
+    if _have_mp_queue:
+        return _id
+    else:
+        return unittest.skip("requires a functioning shared semaphore"
+                              " implementation")
+
 def _parse_guards(guards):
     # Returns a tuple ({platform_name: run_me}, default_value)
     if not guards:
diff -r 1940b72b0a02 Lib/test/test_logging.py
--- a/Lib/test/test_logging.py	Tue Nov 08 20:34:22 2016 +0200
+++ b/Lib/test/test_logging.py	Fri Nov 11 16:31:53 2016 +0100
@@ -3124,6 +3124,7 @@
             self.assertEqual(mock_handle.call_count, 5 * self.repeat,
                              'correct number of handled log messages')
 
+        @support.requires_multiprocessing_queue()
         @patch.object(logging.handlers.QueueListener, 'handle')
         def test_handle_called_with_mp_queue(self, mock_handle):
             for i in range(self.repeat):
@@ -3140,6 +3141,7 @@
             except queue.Empty:
                 return []
 
+        @support.requires_multiprocessing_queue()
         def test_no_messages_in_queue_after_stop(self):
             """
             Five messages are logged then the QueueListener is stopped. This