We present Atacama Large Millimeter/submillimeter Array (ALMA) CO(2-1) spectroscopy of six massive (log(10) M-*/M-circle dot > 11.3) quiescent galaxies at z similar to 1.5. These data represent the largest sample using CO emission to trace molecular gas in quiescent galaxies above z > 1, achieving an average 3 sigma sensitivity of M-H2 similar to 10(10)M(circle dot). We detect one galaxy at 4 sigma significance and place upper limits on the molecular gas reservoirs of the other five, finding molecular gas mass fractions M-H2/M-* = f(H2) <2%-6% (3 sigma upper limits). This is 1-2 orders of magnitude lower than coeval star-forming galaxies at similar stellar.mass, and comparable to galaxies at z.=.0 with similarly low specific star formation rate (sSFR). This indicates that their molecular gas reservoirs were rapidly and efficiently used up or destroyed, and that gas fractions are uniformly low ( 12 by z similar to 4 that halt the accretion of baryons early in the universe. Our data are consistent with a simple picture where galaxies truncate accretion and then consume the existing gas at or faster than typical main-sequence rates. Alternatively, we cannot rule out that these galaxies reside in lower.mass halos, and low gas fractions may instead reflect either stronger feedback, or more efficient gas consumption.