Phase-resolved spectroscopy of the newly discovered X-ray transient MAXI J0556-332 has revealed the presence of narrow emission lines in the Bowen region that most likely arise on the surface of the mass donor star in this low-mass X-ray binary. A period search of the radial velocities of these lines provides two candidate orbital periods (16.43 ± 0.12 and 9.754 ± 0.048 h), which differ from any potential X-ray periods reported. Assuming that MAXI J0556-332 is a relatively high-inclination system that harbours a precessing accretion disc in order to explain its X-ray properties, it is only possible to obtain a consistent set of system parameters for the longer period. These assumptions imply a mass ratio of q≃ 0.45, a radial velocity semi-amplitude of the secondary of K2≃ 190 km s-1 and a compact object mass of the order of the canonical neutron star mass, making a black hole nature for MAXI J0556-332 unlikely. We also report the presence of strong N III emission lines in the spectrum, thereby inferring a high N/O abundance. Finally, we note that the strength of all emission lines shows a continuing decay over the ≃1 month of our observations.