We present high spatial resolution imaging of the CO ( 1–0 ) line from the Karl G. Jansky Very Large Array ( VLA ) of COSMOS 27289 , a massive , compact star forming galaxy at z = 2.234 . This galaxy was selected to be structurally similar to z \sim 2 passive galaxies . Our previous observations showed that it is very gas-poor with respect to typical star-forming galaxies 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 f _ { H _ { 2 } } \equiv M _ { H _ { 2 } } / M _ { star } and the molecular gas depletion time t _ { dep } \equiv M _ { H _ { 2 } } / SFR are lower in the central 1–2 kpc of the galaxy and rise at larger radii \sim 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 \sim 2 quiescent galaxies .