  We have computed, based on 17 infrared radial velocities, the first set of
orbital elements for the M giant in the symbiotic binary V2116 Ophiuchi. The
giant's companion is a neutron star, the bright X-ray source GX 1+4. We find an
orbital period of 1161 days by far the longest of any known X-ray binary. The
orbit has a modest eccentricity of 0.10 with an orbital circularization time of
less than 10^6 years. The large mass function of the orbit significantly
restricts the mass of the M giant. Adopting a neutron-star mass of 1.35M(Sun),
the maximum mass of the M giant is 1.22M(Sun), making it the less massive star.
Derived abundances indicate a slightly subsolar metallicity. Carbon and
nitrogen are in the expected ratio resulting from the red-giant first dredge-up
phase. The lack of O-17 suggests that the M-giant has a mass less than
1.3M(Sun), consistent with our maximum mass. The red giant radius is 103R(Sun),
much smaller than the estimated Roche lobe radius. Thus, the mass loss of the
red giant is via a stellar wind. Although the M giant companion to the neutron
star has a mass similar to the late-type star in low-mass X-ray binaries, its
near-solar abundances and apparent runaway velocity are not fully consistent
with the properties of this class of stars.
