  We use QCD sum-rules to predict ground state masses for pseudoscalar
($J^{PC}=0^{-+}$) charmonium and bottomonium hybrids. We find that the
inclusion of a six-dimensional gluon condensate contribution is needed to
stabilize the analyses. For the charmonium hybrid, we find a mass of
$(3.82\pm0.13)$ GeV; for the bottomonium hybrid, we find a mass of
$(10.64\pm0.19)$ GeV. We comment on possible phenomenological implications
concerning the Y(3940).
