diff --git a/src/flake8/checker.py b/src/flake8/checker.py
index d993cb9..ea8b5d3 100644
--- a/src/flake8/checker.py
+++ b/src/flake8/checker.py
@@ -9,7 +9,7 @@ import tokenize
 from typing import Dict, List, Optional, Tuple
 
 try:
-    import multiprocessing
+    import multiprocessing.pool
 except ImportError:
     multiprocessing = None  # type: ignore
 
@@ -262,18 +262,16 @@ class Manager(object):
             results_found += len(results)
         return (results_found, results_reported)
 
-    def run_parallel(self):
+    def run_parallel(self):  # type: () -> None
         """Run the checkers in parallel."""
         # fmt: off
         final_results = collections.defaultdict(list)  # type: Dict[str, List[Tuple[str, int, int, str, Optional[str]]]]  # noqa: E501
-        final_statistics = collections.defaultdict(dict)  # type: Dict[str, Dict[str, None]]  # noqa: E501
+        final_statistics = collections.defaultdict(dict)  # type: Dict[str, Dict[str, int]]  # noqa: E501
         # fmt: on
 
-        try:
-            pool = multiprocessing.Pool(self.jobs, _pool_init)
-        except OSError as oserr:
-            if oserr.errno not in SERIAL_RETRY_ERRNOS:
-                raise
+        pool = _try_initialize_processpool(self.jobs)
+
+        if pool is None:
             self.run_serial()
             return
 
@@ -303,12 +301,12 @@ class Manager(object):
             checker.results = final_results[filename]
             checker.statistics = final_statistics[filename]
 
-    def run_serial(self):
+    def run_serial(self):  # type: () -> None
         """Run the checkers in serial."""
         for checker in self.checkers:
             checker.run_checks()
 
-    def run(self):
+    def run(self):  # type: () -> None
         """Run all the checkers.
 
         This will intelligently decide whether to run the checks in parallel
@@ -634,11 +632,25 @@ class FileChecker(object):
                     self.run_physical_checks(line + "\n")
 
 
-def _pool_init():
+def _pool_init():  # type: () -> None
     """Ensure correct signaling of ^C using multiprocessing.Pool."""
     signal.signal(signal.SIGINT, signal.SIG_IGN)
 
 
+def _try_initialize_processpool(job_count):
+    # type: (int) -> Optional[multiprocessing.pool.Pool]
+    """Return a new process pool instance if we are able to create one."""
+    try:
+        return multiprocessing.Pool(job_count, _pool_init)
+    except OSError as err:
+        if err.errno not in SERIAL_RETRY_ERRNOS:
+            raise
+    except ImportError:
+        pass
+
+    return None
+
+
 def calculate_pool_chunksize(num_checkers, num_jobs):
     """Determine the chunksize for the multiprocessing Pool.
 
diff --git a/tests/integration/test_checker.py b/tests/integration/test_checker.py
index 0acdb6e..836b543 100644
--- a/tests/integration/test_checker.py
+++ b/tests/integration/test_checker.py
@@ -246,3 +246,38 @@ def test_report_order(results, expected_order):
     with mock.patch.object(manager, '_handle_results', handler):
         assert manager.report() == (len(results), len(results))
         handler.assert_called_once_with('placeholder', expected_results)
+
+
+def test_acquire_when_multiprocessing_pool_can_initialize():
+    """Verify successful importing of hardware semaphore support.
+
+    Mock the behaviour of a platform that has a hardware sem_open
+    implementation, and then attempt to initialize a multiprocessing
+    Pool object.
+
+    This simulates the behaviour on most common platforms.
+    """
+    with mock.patch("multiprocessing.Pool") as pool:
+        result = checker._try_initialize_processpool(2)
+
+    pool.assert_called_once_with(2, checker._pool_init)
+    assert result is pool.return_value
+
+
+def test_acquire_when_multiprocessing_pool_can_not_initialize():
+    """Verify unsuccessful importing of hardware semaphore support.
+
+    Mock the behaviour of a platform that has not got a hardware sem_open
+    implementation, and then attempt to initialize a multiprocessing
+    Pool object.
+
+    This scenario will occur on platforms such as Termux and on some
+    more exotic devices.
+
+    https://github.com/python/cpython/blob/4e02981de0952f54bf87967f8e10d169d6946b40/Lib/multiprocessing/synchronize.py#L30-L33
+    """
+    with mock.patch("multiprocessing.Pool", side_effect=ImportError) as pool:
+        result = checker._try_initialize_processpool(2)
+
+    pool.assert_called_once_with(2, checker._pool_init)
+    assert result is None