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Currently namedtuple(https://hg.python.org/cpython/file/3.5/Lib/collections/__init__.py#l418) sets the `__module__` attribute by looking up `__name__` in calling frame's globals. As in the case of `typing.NamedTuple` it is always going to be 'typing' pickle will raise an error.
Instead of this `typing.NamedTuple` should override the `__module__` attribute itself because it has info about the actual caller frame.
Something like this should work fine:
```
def NamedTuple(typename, fields):
 fields = [(n, t) for n, t in fields]
 cls = collections.namedtuple(typename, [n for n, t in fields])
 cls._field_types = dict(fields)
 try:
 cls.__module__ = sys._getframe(1).f_globals.get('__name__', '__main__')
 except (AttributeError, ValueError):
 pass
 return cls
```
Related: http://stackoverflow.com/q/33796490/846892 

Attached patch.

New changeset 33df0056c148 by Guido van Rossum in branch '3.5':
Issue #25665: Make NamedTuple picklable.
https://hg.python.org/cpython/rev/33df0056c148
New changeset 8a32d44b8359 by Guido van Rossum in branch 'default':
Issue #25665: Make NamedTuple picklable. (Merge 3.5->3.6)
https://hg.python.org/cpython/rev/8a32d44b8359 

Fixed it! Thanks for the report *and* the patch. I wrote a different test though.

The test tests pickling only with default protocol. It would be better to test pickling with all supported protocols.
Why special TestCase methods to check for and report failures are not used in test_typing?

Serhiy, feel free to commit that patch. I was just being lazy. Also, I was using assert instead of self.assertEquals etc. out of laziness (and because at Dropbox people have got the py.test religion and prefer to use assert statements -- but I'm not keen to do this for the stdlib).

New changeset 4f30b0d47c24 by Serhiy Storchaka in branch '3.5':
Issue #25665: Test pickling with all protocols in test_typing.
https://hg.python.org/cpython/rev/4f30b0d47c24
New changeset 9e65015582a5 by Serhiy Storchaka in branch 'default':
Issue #25665: Test pickling with all protocols in test_typing.
https://hg.python.org/cpython/rev/9e65015582a5