A decade of study has established that the molecular gas properties of star-forming galaxies follow coherent scaling relations out to z ∼ 3, suggesting remarkable regularity of the interplay between molecular gas, star formation, and stellar growth. Passive galaxies, however, are expected to be gas-poor and therefore faint, and thus little is known about molecular gas in passive galaxies beyond the local universe. Here we present deep Atacama Large Millimeter/submillimeter Array observations of CO(2-1) emission in eight massive (M star ∼ 1011 M o) galaxies at z ∼ 0.7 selected to lie a factor of 3-10 below the star-forming sequence at this redshift, drawn from the Large Early Galaxy Astrophysics Census survey. We significantly detect half the sample, finding molecular gas fractions ≲0.1. We show that the molecular and stellar rotational axes are broadly consistent, arguing that the molecular gas was not accreted after the galaxies became quiescent. We find that scaling relations extrapolated from the star-forming population overpredict both the gas fraction and gas depletion time for passive objects, suggesting the existence of either a break or large increase in scatter in these relations at low specific star formation rate. Finally, we show that the gas fractions of the passive galaxies we have observed at intermediate redshifts are naturally consistent with evolution into local, massive early-type galaxies by continued low-level star formation, with no need for further gas accretion or dynamical stabilization of the gas reservoirs in the intervening 6 billion years.