  We have identified the third known accretion-powered millisecond pulsar, XTE
J0929-314, with the Rossi X-Ray Timing Explorer. The source is a faint,
high-Galactic-latitude X-ray transient (d >~ 5 kpc) that was in outburst during
2002 April-June. The 185 Hz (5.4 ms) pulsation had a fractional rms amplitude
of 3-7% and was generally broad and sinusoidal, although occasionally
double-peaked. The hard X-ray pulses arrived up to 770 microseconds earlier
than the soft X-ray pulses. The pulsar was spinning down at an average rate of
-(9.2 +/- 0.4) * 10^-14 Hz/s; the spin-down torque may arise from magnetic
coupling to the accretion disk, a magnetohydrodynamic wind, or gravitational
radiation from the rapidly spinning pulsar. The pulsations were modulated by a
43.6 min ultracompact binary orbit, yielding the smallest measured mass
function (2.7 * 10^-7 M_sun) of any stellar binary. The binary parameters imply
an approximately 0.01 M_sun white dwarf donor and a moderately high
inclination. We note that all three known accreting millisecond pulsars are
X-ray transients in very close binaries with extremely low mass transfer rates.
This is an important clue to the physics governing whether or not persistent
millisecond pulsations are detected in low-mass X-ray binaries.
