  The physical mechanisms that quench star formation, turning blue star-forming
galaxies into red quiescent galaxies, remain unclear. In this Letter, we
investigate the role of gas supply in suppressing star formation by studying
the molecular gas content of post-starburst galaxies. Leveraging the wide area
of the SDSS, we identify a sample of massive intermediate-redshift galaxies
that have just ended their primary epoch of star formation. We present ALMA
CO(2-1) observations of two of these post-starburst galaxies at z~0.7 with M* ~
2x10^11 Msun. Their molecular gas reservoirs of (6.4 +/- 0.8) x 10^9 Msun and
(34.0 +/- 1.6) x 10^9 Msun are an order of magnitude larger than
comparable-mass galaxies in the local universe. Our observations suggest that
quenching does not require the total removal or depletion of molecular gas, as
many quenching models suggest. However, further observations are required both
to determine if these apparently quiescent objects host highly obscured star
formation and to investigate the intrinsic variation in the molecular gas
properties of post-starburst galaxies.
