  Binary radio pulsars are superb tools for mapping binary orbits, because of
the precision of the pulse timing method (Taylor and Weisberg 1989). To date,
all orbital parameters for binary pulsars have been derived from observations
of the pulsar alone. We present the first observations of the radial velocity
variations due to the binary motion of a companion to a radio pulsar. Our
results demonstrate that the companion to the Small Magellanic Cloud pulsar PSR
J0045-7319 is the B1V star identified by Kaspi et al. (1994). The mass ratio of
the system is 6.3 +/- 1.2, which, for a neutron star mass of 1.4 Mo, implies a
mass of 8.8 +/- 1.8 Mo for the companion, consistent with the mass expected for
a B1V star. The inclination angle for the binary system is therefore 44 +/- 5
degrees, and the projected rotational velocity of the companion is 113 +/- 10
km/s. The heliocentric radial velocity of the binary system is consistent with
that of other stars and gas in the same region of the Small Magellanic Cloud.
