We present a new nucleosynthesis process that we denote as the nu p process, which occurs in supernovae (and possibly gamma-ray bursts) when strong neutrino fluxes create proton-rich ejecta. In this process, antineutrino absorptions in the proton-rich environment produce neutrons that are immediately captured by neutron-deficient nuclei. This allows for the nucleosynthesis of nuclei with mass numbers A>64, , making this process a possible candidate to explain the origin of the solar abundances of (92,94)Mo and (96,98)Ru. This process also offers a natural explanation for the large abundance of Sr seen in a hyper-metal-poor star.