We report on the optical spectroscopy of the eclipsing halo low-mass X-ray binary 2S 0921-630, which reveals the absorption-line radial velocity curve of the K0 III secondary star with a semiamplitude K2=92.89+/-3.84 km s-1, a systemic velocity γ=34.9+/-3.3 km s-1, and an orbital period Porb of 9.0035+/-0.0029 days (1 σ). Given the quality of the data, we find no evidence for the effects of X-ray irradiation. Using the previously determined rotational broadening of the mass donor and applying conservative limits on the orbital inclination, we constrain the compact object mass to be 2.0-4.3 Msolar (1 σ), ruling out a canonical neutron star at the 99% level. Since the nature of the compact object is unclear, this mass range implies that the compact object is either a low-mass black hole with a mass slightly higher than the maximum possible neutron star mass (2.9 Msolar) or a massive neutron star. If the compact object is a black hole, it confirms the prediction of the existence of low-mass black holes, while if the object is a massive neutron star, its high mass severely constrains the equation of state of nuclear matter.