  The potential enhancement of the cross section $\nu\bar\nu\to e^+e^-$ in the
presence of a magnetic field is of critical interest for the study of
supernovae and as a possible mechanism for gamma ray bursts. While parity
violation(PV) in this reaction in free space is forbidden by CP, the presence
of a CP non-invariant background gas of electrons creates an asymmetry in the
cross section which may contribute to the asymmetry of a supernova and the
natal velocities of neutron stars. We calculate the cross section in the
presence of fields as high as $B = 10^{16}$G and find no significant
enhancement of the cross section with magnetic field strength. By studying the
systematics of our results as a function of environmental variables(field
strength, density,temperature), we extrapolate the relative strength of the
parity violating terms to the weak field limit, and find the parity violation
is insufficient to provide the ``kick'' required to explain the observed
velocities of neutron stars.
