diff --git a/src/twisted/newsfragments/9757.misc b/src/twisted/newsfragments/9757.misc
new file mode 100644
index 000000000..e69de29bb
diff --git a/src/twisted/web/http.py b/src/twisted/web/http.py
index d1b201978..f0fb05b4d 100644
--- a/src/twisted/web/http.py
+++ b/src/twisted/web/http.py
@@ -873,7 +873,8 @@ class Request:
         @type version: C{bytes}
         @param version: The HTTP version of this request.
         """
-        self.content.seek(0,0)
+        clength = self.content.tell()
+        self.content.seek(0, 0)
         self.args = {}
 
         self.method, self.uri = command, path
@@ -889,16 +890,16 @@ class Request:
         # Argument processing
         args = self.args
         ctype = self.requestHeaders.getRawHeaders(b'content-type')
-        clength = self.requestHeaders.getRawHeaders(b'content-length')
         if ctype is not None:
             ctype = ctype[0]
 
-        if clength is not None:
-            clength = clength[0]
-
         if self.method == b"POST" and ctype and clength:
             mfd = b'multipart/form-data'
             key, pdict = _parseHeader(ctype)
+            # This weird CONTENT-LENGTH param is required by
+            # cgi.parse_multipart() in some versions of Python 3.7+, see
+            # bpo-29979. It looks like this will be relaxed and backported, see
+            # https://github.com/python/cpython/pull/8530.
             pdict["CONTENT-LENGTH"] = clength
             if key == b'application/x-www-form-urlencoded':
                 args.update(parse_qs(self.content.read(), 1))
diff --git a/src/twisted/web/newsfragments/9678.bugfix b/src/twisted/web/newsfragments/9678.bugfix
new file mode 100644
index 000000000..141578b7d
--- /dev/null
+++ b/src/twisted/web/newsfragments/9678.bugfix
@@ -0,0 +1 @@
+twisted.web.http.Request now correctly parses multipart-encoded form data submitted as a chunked request on Python 3.7+.
diff --git a/src/twisted/web/test/test_http.py b/src/twisted/web/test/test_http.py
index 6c1b14897..0a0db09b7 100644
--- a/src/twisted/web/test/test_http.py
+++ b/src/twisted/web/test/test_http.py
@@ -1426,6 +1426,73 @@ class ChunkingTests(unittest.TestCase, ResponseTestMixin):
               b"Transfer-Encoding: chunked",
               b"5\r\nHello\r\n6\r\nWorld!\r\n")])
 
+    def runChunkedRequest(self, httpRequest, requestFactory=None,
+                          chunkSize=1):
+        """
+        Execute a web request based on plain text content, chunking
+        the request payload.
+
+        This is a stripped-down, chunking version of ParsingTests.runRequest.
+        """
+        channel = http.HTTPChannel()
+
+        if requestFactory:
+            channel.requestFactory = _makeRequestProxyFactory(requestFactory)
+
+        httpRequest = httpRequest.replace(b"\n", b"\r\n")
+        header, body = httpRequest.split(b"\r\n\r\n", 1)
+
+        transport = StringTransport()
+
+        channel.makeConnection(transport)
+        channel.dataReceived(header+b"\r\n\r\n")
+
+        for pos in range(len(body)//chunkSize+1):
+            if channel.transport.disconnecting:
+                break
+            channel.dataReceived(b"".join(
+                http.toChunk(body[pos*chunkSize:(pos+1)*chunkSize])))
+
+        channel.dataReceived(b"".join(http.toChunk(b"")))
+        channel.connectionLost(IOError("all done"))
+
+        return channel
+
+    def test_multipartFormData(self):
+        """
+        Test that chunked uploads are actually processed into args.
+
+        This is essentially a copy of ParsingTests.test_multipartFormData,
+        just with chunking put in.
+
+        This fails as of twisted version 18.9.0 because of bug #9678.
+        """
+        processed = []
+
+        class MyRequest(http.Request):
+            def process(self):
+                processed.append(self)
+                self.write(b"done")
+                self.finish()
+        req = b'''\
+POST / HTTP/1.0
+Content-Type: multipart/form-data; boundary=AaB03x
+Transfer-Encoding: chunked
+
+--AaB03x
+Content-Type: text/plain
+Content-Disposition: form-data; name="text"
+Content-Transfer-Encoding: quoted-printable
+
+abasdfg
+--AaB03x--
+'''
+        channel = self.runChunkedRequest(req, MyRequest, chunkSize=5)
+        self.assertEqual(channel.transport.value(),
+                         b"HTTP/1.0 200 OK\r\n\r\ndone")
+        self.assertEqual(len(processed), 1)
+        self.assertEqual(processed[0].args, {b"text": [b"abasdfg"]})
+
 
 
 class ParsingTests(unittest.TestCase):
diff --git a/tox.ini b/tox.ini
index 328ac0354..e5fdf779c 100644
--- a/tox.ini
+++ b/tox.ini
@@ -48,9 +48,9 @@ extras =
 deps =
     py27-alldeps-{posix,macos}: pysqlite
 
-    ; Coverage 5.0 does not work with codecov.
-    {withcov}: coverage<5.0
-    {coverage-prepare,codecov-publish}: coverage<5.0
+    {withcov}: coverage
+
+    {coverage-prepare,codecov-publish}: coverage
 
     {codecov-push,codecov-publish}: codecov