We report new radial velocity observations of V779 Cen, the optical companion to the X-ray pulsar Cen X-3. Two sets of results at two epochs yield very different radial velocity amplitudes. We demonstrate there are problems with the first set, not least that they are incompatible with the observed duration of the X-ray eclipse for all inclination angles. The anomalously high radial velocities are probably a result of changes in the outflow behaviour of the companion star. Although there is no reason to doubt the results from the second epoch when viewed in isolation, given the anomalous radial velocities of the first epoch, they must be treated with caution. Using these data, the semi-amplitude of the resulting radial velocity curve is found to be 24.4+/-4.1kms-1. Given the accurately measured semi-amplitude of the orbit of the pulsar, 414.3+/-0.9kms-1, the mass ratio of the system is 0.059+/-0.010. The inclination of the system is found to be 70.2°+/-2.7°, assuming that the optical component fills its Roche lobe, and that the system is in synchronous rotation. Hence the mass of the neutron star is 1.21+/-0.21Msolar, and the mass of the optical companion is 20.5+/-0.7Msolar. This is a smaller uncertainty than previously reported values, and is consistent with the canonical neutron star mass of 1.4Msolar. In addition, we use our spectra to determine the spectral class of V779 Cen to be O6-7II-III.