  We report the discovery of a variable optical and X-ray source within the
error ellipse of the previously unassociated Fermi Large Area Telescope
$\gamma$-ray source 4FGL J0407.7--5702. A 22 ksec observation from
XMM-Newton/EPIC shows an X-ray light curve with rapid variability and flaring.
The X-ray spectrum is well-fit by a hard power law with $\Gamma = 1.7$. Optical
photometry taken over several epochs is dominated by aperiodic variations of
moderate amplitude. Optical spectroscopy with SOAR and Gemini reveals a blue
continuum with broad and double-peaked H and He emission, as expected for an
accretion disk around a compact binary. Overall, the optical, X-ray, and
$\gamma$-ray properties of 4FGL J0407.7--5702 are consistent with a
classification as a transitional millisecond pulsar in the sub-luminous disk
state. We also present evidence that this source is more distant than other
confirmed or candidate transitional millisecond pulsar binaries, and that the
ratio of X-ray to $\gamma$-ray flux is a promising tool to help identify such
binaries, indicating that a more complete census for these rare systems is
becoming possible.
