We consider the possible neutrino emission from SN1987A generated through the process gamma-gamma --> pi-0 --> nu-nuBAR, which is permitted when the neutrinos have a right-handed component. This energy-loss mechanism is consistent with the supernova neutrino observations if the decay rate-GAMMA (pi-0 --> nu-nuBAR) < (0.15-6.3) X 10(-13) eV. When the reaction pi-0 --> nu-nuBAR is mediated by weak gauge bosons the limit on the decay rate allows us to obtain constraints on neutrino masses, m-nu < 5-27 keV, depending on the core temperature.