  One of the greatest challenges to theoretical models of massive galaxy
formation is the regulation of star formation at early times. The relative
roles of molecular gas expulsion, depletion, and stabilization are uncertain as
direct observational constraints of the gas reservoirs in quenched or quenching
galaxies at high redshift are scant. We present ALMA observations of CO(2-1) in
a massive ($\log M_{\star}/M_{\odot}=11.2$), recently quenched galaxy at
$z=1.522$. The optical spectrum of this object shows strong Balmer absorption
lines, which implies that star formation ceased $\sim$0.8 Gyr ago. We do not
detect CO(2-1) line emission, placing an upper limit on the molecular
$\mathrm{H_2}$ gas mass of 1.1$\times10^{10}\,M_{\odot}$. The implied gas
fraction is $f_{\rm{H_2}}{\equiv M_{H_2}/M_{\star}}<7\%$, $\sim10\times$ lower
than typical star forming galaxies at similar stellar masses at this redshift,
among the lowest gas fractions at this specific star formation rate at any
epoch, and the most stringent constraint on the gas contents of a $z>1$ passive
galaxy to date. Our observations show that the depletion of $\mathrm{H_2}$ from
the interstellar medium of quenched objects can be both efficient and fairly
complete, in contrast to recent claims of significant cold gas in recently
quenched galaxies. We explore the variation in observed gas fractions in
high-$z$ galaxies and show that galaxies with high stellar surface density have
low $f_{\rm{H_2}}$, similar to recent correlations between specific star
formation rate and stellar surface density.
