diff --git a/googleapiclient/http.py b/googleapiclient/http.py
index 6a47bf7..9e549de 100644
--- a/googleapiclient/http.py
+++ b/googleapiclient/http.py
@@ -647,6 +647,14 @@
     self._sleep = time.sleep
     self._rand = random.random
 
+    self._headers = {}
+    for k, v in six.iteritems(request.headers):
+      # allow users to supply custom headers by setting them on the request
+      # but strip out the ones that are set by default on requests generated by
+      # API methods like Drive's files().get(fileId=...)
+      if not k.lower() in ('accept', 'accept-encoding', 'user-agent'):
+        self._headers[k] = v
+
   @util.positional(1)
   def next_chunk(self, num_retries=0):
     """Get the next chunk of the download.
@@ -666,10 +674,9 @@
       googleapiclient.errors.HttpError if the response was not a 2xx.
       httplib2.HttpLib2Error if a transport error has occured.
     """
-    headers = {
-        'range': 'bytes=%d-%d' % (
+    headers = self._headers.copy()
+    headers['range'] = 'bytes=%d-%d' % (
             self._progress, self._progress + self._chunksize)
-        }
     http = self._request.http
 
     resp, content = _retry_request(
diff --git a/tests/test_http.py b/tests/test_http.py
index 8a976ee..e381294 100644
--- a/tests/test_http.py
+++ b/tests/test_http.py
@@ -29,6 +29,7 @@
 from six.moves.urllib.parse import urlencode
 
 # Do not remove the httplib2 import
+import json
 import httplib2
 import logging
 import mock
@@ -456,6 +457,41 @@
     self.assertEqual(5, download._progress)
     self.assertEqual(5, download._total_size)
 
+  def test_media_io_base_download_custom_request_headers(self):
+    self.request.http = HttpMockSequence([
+      ({'status': '200',
+        'content-range': '0-2/5'}, 'echo_request_headers_as_json'),
+      ({'status': '200',
+        'content-range': '3-4/5'}, 'echo_request_headers_as_json'),
+    ])
+    self.assertEqual(True, self.request.http.follow_redirects)
+
+    self.request.headers['Cache-Control'] = 'no-store'
+
+    download = MediaIoBaseDownload(
+        fd=self.fd, request=self.request, chunksize=3)
+
+    self.assertEqual(download._headers, {'Cache-Control':'no-store'})
+
+    status, done = download.next_chunk()
+
+    result = self.fd.getvalue().decode('utf-8')
+
+    # we abuse the internals of the object we're testing, pay no attention
+    # to the actual bytes= values here; we are just asserting that the
+    # header we added to the original request is sent up to the server
+    # on each call to next_chunk
+
+    self.assertEqual(json.loads(result),
+                     {"Cache-Control": "no-store", "range": "bytes=0-3"})
+
+    download._fd = self.fd = BytesIO()
+    status, done = download.next_chunk()
+
+    result = self.fd.getvalue().decode('utf-8')
+    self.assertEqual(json.loads(result),
+                     {"Cache-Control": "no-store", "range": "bytes=51-54"})
+
   def test_media_io_base_download_handle_redirects(self):
     self.request.http = HttpMockSequence([
       ({'status': '200',