  High amplitude X-ray brightness oscillations during thermonuclear X-ray
bursts were discovered with the Rossi X-ray Timing Explorer (RXTE) in early
1996. Spectral and timing evidence strongly supports the conclusion that these
oscillations are caused by rotational modulation of the burst emission and that
they reveal the spin frequency of neutron stars in low mass X-ray binaries
(LMXB), a long sought goal of X-ray astronomy. I briefly review the status of
our knowledge of these oscillations. So far 10 neutron star systems have been
observed to produce burst oscillations, interestingly, the observed frequencies
cluster in a fairly narrow range from about 300 - 600 Hz, well below the
break-up frequency for most modern neutron star equations of state (EOS). This
has led to suggestions that their spin frequencies may be limited by the loss
of angular momentum due to gravitational wave emission. Connections with
gravity wave rotational instabilities will be briefly described.
