  We report the discovery by the RXTE PCA of a second transient accreting
millisecond pulsar, XTE J1751-305, during regular monitoring observations of
the galactic bulge region. The pulsar has a spin frequency of 435 Hz, making it
one of the fastest pulsars. The pulsations contain the signature of orbital
Doppler modulation, which implies an orbital period of 42 minutes, the shortest
orbital period of any known radio or X-ray millisecond pulsar. The mass
function, f_x = (1.278 +/- 0.003) x 10^{-6} M_sun, yields a minimum mass for
the companion of between 0.013 and 0.017 M_sun, depending on the mass of the
neutron star. No eclipses were detected. A previous X-ray outburst in June,
1998, was discovered in archival All-Sky Monitor data. Assuming mass transfer
in this binary system is driven by gravitational radiation, we constrain the
orbital inclination to be in the range 30-85 deg, and the companion mass to be
0.013-0.035 M_sun. The companion is most likely a heated helium dwarf. We also
present results from the Chandra HRC-S observations which provide the best
known position of XTE J1751-305.
