We obtained new optical observations of the X-ray source XMMU J083850.38-282756.8, the previously proposed counterpart of the γ-ray source 3FGL J0838.8-2829. Time-series photometry in the r′ band reveals periodic modulation of ~1 mag that is characteristic of the heating of the photosphere of a low-mass companion star by a compact object. The measured orbital period is 5.14817 ± 0.00012 hr. The shape of the light curve is variable, evidently due to the effects of flaring and asymmetric heating. Spectroscopy reveals a companion of type M1 or later, having a radial velocity amplitude of 315 ± 17 km s–1, with period and phasing consistent with the heating interpretation. The mass function of the compact object is 0.69±0.11 M☉, which allows a neutron star in a high-inclination orbit. Variable, broad Hα emission is seen, which is probably associated with a wind from the companion. These properties, as well as the X-ray and γ-ray luminosities at the inferred distance of 1.7 kpc, are consistent with a redback millisecond pulsar in its non-accreting state. A search for radio pulsations is needed to confirm this interpretation and derive complete system parameters for modeling, although absorption by the ionized wind could hinder such detection.