diff --git a/Lib/subprocess.py b/Lib/subprocess.py
index 6cc3fa1..0f284d1 100644
--- a/Lib/subprocess.py
+++ b/Lib/subprocess.py
@@ -1287,9 +1287,16 @@
                     pid, sts = _waitpid(self.pid, _WNOHANG)
                     if pid == self.pid:
                         self._handle_exitstatus(sts)
-                except _os_error:
+                except _os_error as e:
                     if _deadstate is not None:
                         self.returncode = _deadstate
+                    if e.errno == errno.ECHILD:
+                        # This happens if SIGCLD is set to be ignored or
+                        # waiting for child processes has otherwise been
+                        # disabled for our process.  This child is dead, we
+                        # can't get the status.
+                        # http://bugs.python.org/issue15756
+                        self.returncode = 0
             return self.returncode
 
 
diff --git a/Lib/test/subprocessdata/sigchild_ignore.py b/Lib/test/subprocessdata/sigchild_ignore.py
index 6072aec..86320fb 100644
--- a/Lib/test/subprocessdata/sigchild_ignore.py
+++ b/Lib/test/subprocessdata/sigchild_ignore.py
@@ -1,6 +1,15 @@
-import signal, subprocess, sys
+import signal, subprocess, sys, time
 # On Linux this causes os.waitpid to fail with OSError as the OS has already
 # reaped our child process.  The wait() passing the OSError on to the caller
 # and causing us to exit with an error is what we are testing against.
 signal.signal(signal.SIGCHLD, signal.SIG_IGN)
 subprocess.Popen([sys.executable, '-c', 'print("albatross")']).wait()
+# Also ensure poll() handles an errno.ECHILD appropriately.
+p = subprocess.Popen([sys.executable, '-c', 'print("albatross")'])
+num_polls = 0
+while p.poll() is None:
+    # Waiting for the process to finish.
+    time.sleep(0.01)  # Avoid being a CPU busy loop.
+    num_polls += 1
+    if num_polls > 3000:
+        raise RuntimeError('poll should have returned 0 within 30 seconds')
diff --git a/Misc/NEWS b/Misc/NEWS
index d6aa34b..e46b9a5 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -113,6 +113,10 @@
 Library
 -------
 
+- Issue #15756: subprocess.poll() now properly handles errno.ECHILD to
+  return a returncode of 0 when the child has already exited or cannot
+  be waited on.
+
 - Issue #12376: Pass on parameters in TextTestResult.__init__ super call
 
 - Issue #15222: Insert blank line after each message in mbox mailboxes