  Many neutron stars are observed to be moving with spatial velocities, in
excess of 500km/s. A number of mechanisms have been proposed to give neutron
stars these high velocities. One of the leading classes of models proposed
invokes asymmetries in the core of a massive star just prior to collapse. These
asymmetries grow during the collapse, causing the resultant supernova to also
be asymmetric. As the ejecta is launched, it pushes off (or ``kicks'') the
newly formed neutron star. This paper presents the first 3-dimensional
supernova simulations of this process. The ejecta is not the only matter that
kicks the newly-formed neutron star. Neutrinos also carry away momentum and the
asymmetric collapse leads also to asymmetries in the neutrinos. However, the
neutrino asymmetries tend to damp out the neutron star motions and even the
most extreme asymmetric collapses presented here do not produce final neutron
star velocities above 200km/s.
