  A three-dimensional, Newtonian hydrodynamic technique is used to follow the
postbounce phase of a stellar core collapse event. For realistic initial data
we have employed post core-bounce snapshots of the iron core of a 20 solar mass
star. The models exhibit strong differential rotation but have centrally
condensed density stratifications. We demonstrate for the first time that such
postbounce cores are subject to a so-called low-T/|W| nonaxisymmetric
instability and, in particular, can become dynamically unstable to an m=1 -
dominated spiral mode at T/|W| ~ 0.08. We calculate the gravitational wave
emission by the instability and find that the emitted waves may be detectable
by current and future GW observatories from anywhere in the Milky Way.
