This only seems to be the case with the C implementation of json (_json). 

>>> json.encoder.c_make_encoder = None
>>> json.dumps(OrderedDict(items))
'{"one": 1, "two": 2, "three": 3, "four": 4, "five": 5}'

I think the culprit is encoder_listencode_dict (Modules/_json.c:2049).
It uses PyDict_Next to fetch all items from the dictionary and thereby
loses order. A special code branch for dict subclasses
(!PyDict_CheckExact) which uses PyIter* instead should solve the
problem. (PyDict_Next should not honor order no matter what IMO.)

If nobody beats me to it I can try to come up with a patch.