  We report the results of a search for burst oscillations during thermonuclear
X-ray bursts from the low mass X-ray binary (LMXB) EXO 0748-676. With the
proportional counter array (PCA) onboard the Rossi X-ray Timing Explorer (RXTE)
we detected a 45 Hz oscillation in the average power spectrum of 38
thermonuclear X-ray bursts from this source. We computed power spectra with 1
Hz frequency resolution for both the rising and decaying portions of 38 X-ray
bursts from the public RXTE archive. We averaged the 1 Hz power spectra and
detected a significant signal at 45 Hz in the decaying phases of the bursts.
The signal is detected at a significance level of 4 x 10^-8. No similar signal
was detected in the rising intervals. A fit to the oscillation peak at 0.25 Hz
resolution gives a frequency of 44.7 +/- 0.06 Hz and an oscillation quality
factor of Q = 80 +/- 18. The average signal amplitude is 3% (rms). The
detection of 45 Hz burst oscillations from EXO 0748-676 provides compelling
evidence that this is the neutron star spin frequency in this system. We use
the inferred spin frequency to model the widths of absorption lines from the
neutron star surface and show that the widths of the absorption lines from EXO
0748-676 recently reported by Cottam et al. are consistent with a 45 Hz spin
frequency as long as the neutron star radius is in the range from about 9.5-15
km. With a known spin frequency, precise modelling of the line profiles from
EXO 0748-676 holds great promise for constraining the dense matter equation of
state.
