[FOM] Hahn Banach and the Baire Property

[D.R. MacIver]

Does anyone happen to know (and ideally have a cite for) whether it is 
known if the Hahn Banach theorem implies the existence of a subset of R 
without the Baire Property (in ZF say)? I'm presuming it does, as it proves 
the existence of a non-measurable subset of R, but I can't seem to find a 
reference one way or the other.

(Sorry for the rather analysis-like question, but I think it really is 
still FOM. Especially as it's entirely possible that the only way to answer 
it is to construct a certain model of set theory!)

Thanks,
David R. MacIver