Neutrino oscillations, biased by the magnetic field, alter the shape o
f the neutrinosphere in a cooling protoneutron star emerging from the
supernova collapse. The resulting anisotropy in the momentum of outgoi
ng neutrinos can be the origin of the observed proper motions of pulsa
rs. The connection between the pulsar velocities and neutrino oscillat
ions results in a prediction for the tau neutrino mass of m(nu(tau)) s
imilar to 100 eV.