In a relativistic plasma, neutrinos can emit plasmons by the Cherenkov
process which is kinematically allowed for a range of frequencies for
which the refractive index is greater than one. We calculate the rate
of energy emission by this process. We compute the energy deposited i
n a stalled supernova shock wave by the Cherenkov process and find tha
t it is much smaller than the Bethe-Wilson mechanism.