  Dynamical instability is shown to occur in differentially rotating polytropes
with N = 3.33 and $T/|W| \gtrsim 0.14$. This instability has a strong m=1 mode,
although the m=2, 3, and 4 modes also appear. Such instability may allow a
centrifugally-hung core to begin collapsing to neutron star densities on a
dynamical timescale. The gravitational radiation emitted by such unstable cores
may be detectable with advanced ground-based detectors, such as LIGO II. If the
instability occurs in a supermassive star, it may produce gravitational
radiation detectable by the space-based detector LISA.
