Is Parity-P contained in PP? This question was asked by Jan Pax on the Foundations of Mathematics mailing list.
Certainly $P^{\oplus P} \subseteq P^{\#P} = P^{PP}$
but I suspect from the answers to this question that it's not known whether $\oplus P \subseteq PP$ (otherwise, $PP$ would be one possible answer to that question).  If it's not known, is there an oracle separation?
Scott Aaronson gives an oracle where $\oplus$P = PEXP which implies the oracle you want. http://eccc.hpi-web.de/report/2005/040/download/ (Theorem 12 in the appendix)