diff --git a/Lib/test/test_multiprocessing.py b/Lib/test/test_multiprocessing.py
--- a/Lib/test/test_multiprocessing.py
+++ b/Lib/test/test_multiprocessing.py
@@ -105,6 +105,10 @@
 except:
     MAXFD = 256
 
+
+# An upper bound on the maximum number of semaphores needed by this test.
+MAX_SEMS = 30
+
 #
 # Some tests require ctypes
 #
@@ -115,6 +119,21 @@
     Structure = object
     c_int = c_double = None
 
+
+def check_enough_semaphores():
+    """Check that the system supports enough semaphores to run the test."""
+    sems = []
+    for i in range(MAX_SEMS):
+        try:
+            sem = multiprocessing.Semaphore()
+            sems.append(sem)
+        except OSError as e:
+            if e.errno == errno.ENFILE:
+                raise unittest.SkipTest("The OS doesn't support enough semaphores "
+                                        "to run the test.")
+            raise
+
+
 #
 # Creates a wrapper for a function which records the time it takes to finish
 #
@@ -2349,6 +2368,8 @@
         except OSError:
             raise unittest.SkipTest("OSError raises on RLock creation, see issue 3111!")
 
+    check_enough_semaphores()
+
     if run is None:
         from test.support import run_unittest as run