We report the discovery of a variable optical and X-ray source within the error ellipse of the previously unassociated Fermi Large Area Telescope γ-ray source 4FGL J0407.7-5702. A 22 ks observation from XMM-Newton/European Photon Imaging Camera (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 Γ = 1.7. Optical photometry taken over several epochs is dominated by aperiodic variations of moderate amplitude. Optical spectroscopy with Southern Astrophysical Research (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 γ-ray properties of 4FGL J0407.7-5702 are consistent with a classification as a transitional millisecond pulsar in the subluminous 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 γ-ray flux is a promising tool to help identify such binaries, indicating that a more complete census for these rare systems is becoming possible.