Abstract We have discovered a new X-ray-emitting compact binary that is the likely counterpart to the unassociated Fermi-LAT GeV γ -ray source 4FGL J1120.0–2204, the second brightest Fermi source that still remains formally unidentified. Using optical spectroscopy with the SOAR telescope, we have identified a warm ( T eff ∼ 8500 K) companion in a 15.1 hr orbit around an unseen primary, which is likely a yet-undiscovered millisecond pulsar. A precise Gaia parallax shows the binary is nearby, at a distance of only ∼820 pc. Unlike the typical “spider” or white dwarf secondaries in short-period millisecond pulsar binaries, our observations suggest the ∼0.17 M ⊙ companion is in an intermediate stage, contracting on the way to becoming an extremely low-mass helium white dwarf. Although the companion is apparently unique among confirmed or candidate millisecond pulsar binaries, we use binary evolution models to show that in ∼2 Gyr, the properties of the binary will match those of several millisecond pulsar–white dwarf binaries with very short (<1 day) orbital periods. This makes 4FGL J1120.0–2204 the first system discovered in the penultimate phase of the millisecond pulsar recycling process.