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 \pm 0.003 ) \times 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° , 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 .