Superconductivity at temperatures up to 190 K at high pressures has recently been observed in H2S and interpreted as conventional BCS-electron-phonon-driven superconductivity.\cite{h2s} Instead we propose that it is another example of the mechanism of hole superconductivity at work. Within this mechanism high temperature superconductivity arises when holes conduct through negatively charged anions in close proximity. We propose that electron transfer from H to S leads to conduction by holes in a nearly full band arising from direct overlap of S= p orbitals in a planar structure. The superconductivity is non-phononic and is driven by pairing of heavily dressed hole carriers to lower their kinetic energy. Possible explanations for the observed lower critical temperature of D2S are discussed. We predict that high temperature superconductivity will also be found in other sulfides under high pressure such as Li2S, Na2S and K2S.