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We have discovered a new X-ray emitting compact binary that is the likelycounterpart to the unassociated Fermi-LAT GeV $\gamma$-ray source 4FGLJ1120.0-2204, the second brightest Fermi source that still remains formallyunidentified. Using optical spectroscopy with the SOAR telescope, we haveidentified a warm ($T_{\textrm{eff}}\sim8500$ K) companion in a 15.1-hr orbitaround an unseen primary, which is likely a yet-undiscovered millisecondpulsar. A precise Gaia parallax shows the binary is nearby, at a distance ofonly $\sim 820$ pc. Unlike the typical "spider" or white dwarf secondaries inshort-period millisecond pulsar binaries, our observations suggest the $\sim0.17\,M_{\odot}$ companion is in an intermediate stage, contracting on the wayto becoming an extremely low-mass helium white dwarf (a "pre-ELM" white dwarf).Although the companion is apparently unique among confirmed or candidatemillisecond pulsar binaries, we use binary evolution models to show that in$\sim 2$ Gyr, the properties of the binary will match those of severalmillisecond pulsar-white dwarf binaries with very short ($< 1$ d) orbitalperiods. This makes 4FGL J1120.0-2204 the first system discovered in thepenultimate phase of the millisecond pulsar recycling process.

4FGL J1120.0-2204: A Unique Gamma-ray Bright Neutron Star Binary with an Extremely Low Mass Proto-White Dwarf