  We present high spatial resolution imaging of the CO(1-0) line from the Karl
G. Jansky Very Large Array (VLA) of COSMOS27289, a massive, compact star
forming galaxy at z=2.234. This galaxy was selected to be structurally similar
to z~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_H2 =
M_H2/M_star and the molecular gas depletion time t_dep = M_H2/SFR are lower in
the central 1-2kpc of the galaxy and rise at larger radii ~2-4kpc. These
observations are consistent with a scenario in which COSMOS27289 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.
