  We obtained new optical observations of the X-ray source XMMU
J083850.38-282756.8, the previously proposed counterpart of the gamma-ray
source 3FGL J0838.8-2829. Time-series photometry in the $r'$ band reveals
periodic modulation of $\approx1$ magnitude 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$\pm$0.00012 hr. The shape of the light
curve is variable, evidently due to the effects of flaring and asymmetric
heating. Spectroscopy reveals a companion of type M1 or later, having a radial
velocity amplitude of 315$\pm$17 km/s, with period and phasing consistent with
the heating interpretation. The mass function of the compact object is
0.69$\pm$0.11 $M_{\odot}$, which allows a neutron star in a high-inclination
orbit. Variable, broad H$\alpha$ emission is seen, which is probably associated
with a wind from the companion. These properties, as well as the X-ray and
gamma-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.
