  LMC P3 is the most luminous gamma-ray binary discovered to date and the first
detected outside of the Galaxy, with an orbital period of 10.301 d. We report
on optical spectroscopic observations undertaken with the Southern African
Large Telescope (SALT) using the High Resolution spectrograph (HRS). We find
the binary is slightly eccentric, $e = 0.40\pm0.07$, and place the time of
periastron at HJD $2457412.13 \pm 0.29$. Stellar model fitting finds an
effective temperature of $T_{\rm eff} = 36351 \pm 53$ K. The mass function, $f
= 0.0010 \pm 0.0004$ M$_{\odot}$, favours a neutron star compact object. The
phases of superior and inferior conjunctions are $0.98$ and $0.24$,
respectively (where phase 0 is at the Fermi-LAT maximum), close to the reported
maxima in the GeV and TeV light curves.
