We have observed the persistent but optically unidentified X-ray source X1908+075 with the PCA and HEXTE instruments on RXTE . The binary nature of this source was established by ( ) who found a 4.4-day orbital period in results from the RXTE ASM . We report the discovery of 605 s pulsations in the X-ray flux . The Doppler delay curve is measured and provides a mass function of 6.1 M _ { \sun } which is a lower limit to the mass of the binary companion of the neutron star . The degree of attenuation of the low-energy end of the spectrum is found to be a strong function of orbital phase . A simple model of absorption in a stellar wind from the companion star fits the orbital phase dependence reasonably well and limits the orbital inclination angle to the range 38 \arcdeg - 72 \arcdeg . These measured parameters lead to an orbital separation of \sim 60 - 80 lt-s , a mass for the companion star in the range 9-31 M _ { \sun } , and an upper limit to the size of the companion of \sim 22 ~ { } R _ { \sun } . From our analysis we also infer a wind mass loss rate from the companion star of \gtrsim 1.3 \times 10 ^ { -6 } ~ { } M _ { \sun } yr ^ { -1 } and , when the properties of the companion star and the effects of photoionization are considered , likely \gtrsim 4 \times 10 ^ { -6 } ~ { } M _ { \sun } yr ^ { -1 } . Such a high rate is inconsistent with the allowed masses and radii that we find for a main sequence or modestly evolved star unless the mass loss rate is enhanced in the binary system relative to that of an isolated star . We discuss the possibility that the companion might be a Wolf-Rayet star that could evolve to become a black hole in 10 ^ { 4 } to 10 ^ { 5 } yr . If so , this would be the first identified progenitor of a neutron star–black hole binary .