diff --git a/CHANGES.rst b/CHANGES.rst
index f02becbed1..5170e82aeb 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -21,9 +21,14 @@ https://github.com/zopefoundation/Zope/blob/4.x/CHANGES.rst
 - Fix ``OFS.Image.File.__str__`` for ``Pdata`` contents
   (`#711 <https://github.com/zopefoundation/Zope/issues/711>`_)
 
+- Add ``wsgi.file_wrapper`` implementation
+  https://www.python.org/dev/peps/pep-0333/#optional-platform-specific-file-handling
+  (`#719 <https://github.com/zopefoundation/Zope/pull/719>`_)
+
 - Set ``REMOTE_USER`` in wsgi environ using Zope user authentication
   (`#713 <https://github.com/zopefoundation/Zope/pull/713>`_)
 
+
 - Improve documentation for Zope's error logging services.
 
 Backwards incompatible changes
diff --git a/src/ZPublisher/WSGIPublisher.py b/src/ZPublisher/WSGIPublisher.py
index af0cbddc4d..7bde076370 100644
--- a/src/ZPublisher/WSGIPublisher.py
+++ b/src/ZPublisher/WSGIPublisher.py
@@ -351,7 +351,10 @@ def publish_module(environ, start_response,
 
         if isinstance(response.body, _FILE_TYPES) or \
            IUnboundStreamIterator.providedBy(response.body):
-            result = response.body
+            if 'wsgi.file_wrapper' in environ:
+                result = environ['wsgi.file_wrapper'](response.body)
+            else:
+                result = response.body
         else:
             # If somebody used response.write, that data will be in the
             # response.stdout BytesIO, so we put that before the body.
diff --git a/src/ZPublisher/tests/test_WSGIPublisher.py b/src/ZPublisher/tests/test_WSGIPublisher.py
index 9c45fc8f8d..76d57741cb 100644
--- a/src/ZPublisher/tests/test_WSGIPublisher.py
+++ b/src/ZPublisher/tests/test_WSGIPublisher.py
@@ -445,6 +445,73 @@ def __next__(self):
         app_iter = self._callFUT(environ, start_response, _publish)
         self.assertTrue(app_iter is body)
 
+    def test_stream_file_wrapper(self):
+        from ZPublisher.Iterators import IStreamIterator
+        from zope.interface import implementer
+        from ZPublisher.HTTPResponse import WSGIResponse
+
+        @implementer(IStreamIterator)
+        class TestStreamIterator(object):
+            data = "hello" * 20
+
+            def __len__(self):
+                return len(self.data)
+
+        class Wrapper(object):
+            def __init__(self, file):
+                self.file = file
+
+        _response = WSGIResponse()
+        _response.setHeader('Content-Type', 'text/plain')
+        body = _response.body = TestStreamIterator()
+        environ = self._makeEnviron(**{'wsgi.file_wrapper': Wrapper})
+        start_response = DummyCallable()
+        _publish = DummyCallable()
+        _publish._result = _response
+        app_iter = self._callFUT(environ, start_response, _publish)
+        self.assertTrue(app_iter.file is body)
+        self.assertTrue(isinstance(app_iter, Wrapper))
+        self.assertEqual(
+            int(_response.headers['content-length']), len(body))
+        self.assertTrue(
+            _response.headers['content-type'].startswith('text/plain'))
+        self.assertEqual(_response.status, 200)
+
+    def test_unboundstream_file_wrapper(self):
+        from ZPublisher.Iterators import IUnboundStreamIterator
+        from zope.interface import implementer
+        from ZPublisher.HTTPResponse import WSGIResponse
+
+        @implementer(IUnboundStreamIterator)
+        class TestUnboundStreamIterator(object):
+            data = "hello"
+
+            def __len__(self):
+                return len(self.data)
+
+        class Wrapper(object):
+            def __init__(self, file):
+                self.file = file
+
+        _response = WSGIResponse()
+        _response.setStatus(200)
+        # UnboundStream needs Content-Length header
+        _response.setHeader('Content-Length', '5')
+        _response.setHeader('Content-Type', 'text/plain')
+        body = _response.body = TestUnboundStreamIterator()
+        environ = self._makeEnviron(**{'wsgi.file_wrapper': Wrapper})
+        start_response = DummyCallable()
+        _publish = DummyCallable()
+        _publish._result = _response
+        app_iter = self._callFUT(environ, start_response, _publish)
+        self.assertTrue(app_iter.file is body)
+        self.assertTrue(isinstance(app_iter, Wrapper))
+        self.assertEqual(
+            int(_response.headers['content-length']), len(body))
+        self.assertTrue(
+            _response.headers['content-type'].startswith('text/plain'))
+        self.assertEqual(_response.status, 200)
+
     def test_request_closed(self):
         environ = self._makeEnviron()
         start_response = DummyCallable()