  For neutrinos with a magnetic moment, we show that the collisions in a hot
and dense plasma act as an efficient mechanism for the conversion of $\nu_L$
into $\nu_R$. The production rate for right-handed neutrinos is computed in
terms of a resummed photon propagator which consistently incorporates the
background effects. Assuming that the entire energy in a supernova collapse is
not carried away by the $\nu_R$, our results can be used to place an upper
limit on the neutrino magnetic moment $\mu_\nu < (0.1-0.4)\times 10^{-11}\mu_B$
