We present high spatial resolution imaging of the CO(1–0) line from the Karl G. Jansky Very Large Array of COSMOS 27289, a massive, compact star-forming galaxy (SFG) at z = 2.234. This galaxy was selected because of its structural similarity to z ~ 2 passive galaxies. Our previous observations showed that it is very gas poor with respect to typical SFGs at these redshifts, consistent with a rapid transition to quiescence as the molecular gas is depleted. The new data show that both the molecular gas fraction, fH2 ≡MH2/Mstar and the molecular gas depletion time, tdep ≡ MH2/SFR are lower in the central 1–2 kpc of the galaxy and rise at larger radii ~2–4 kpc. These observations are consistent with a scenario in which COSMOS 27289 will imminently cease star formation in the inner regions before the outskirts, i.e., inside-out quenching, the first time this phenomenon has been seen via observations of molecular gas in the high-redshift universe. We find good qualitative and quantitative agreement with a hydrodynamical simulation of galaxy quenching, in which the central suppression of molecular gas arises due to rapid gas consumption and outflows that evacuate the central regions of gas. Our results provide independent evidence for inside-out quenching of star formation as a plausible formation mechanism for z ~ 2 quiescent galaxies.