The nature of absorption-selected galaxies and their connection to the general galaxy population have been open issues for more than three decades, with little information available on their gas properties. Here we show, using detections of carbon monoxide (CO) emission with the Atacama Large Millimeter/submillimeter Array (ALMA), that five of seven high-metallicity, absorption-selected galaxies at intermediate redshifts, $z approx 0.5-0.8$, have large molecular gas masses, $M_{rm Mol} approx (0.6 - 8.2) times 10^{10} : {rm M}_odot$ and high molecular gas fractions ($f_{rm Mol} equiv : M_{rm Mol}/(M_ast + M_{rm Mol}) approx 0.29-0.87)$. Their modest star formation rates (SFRs), $approx (0.3-9.5) : {rm M}_odot$ yr$^{-1}$, then imply long gas depletion timescales, $approx (3 - 120)$ Gyr. The high-metallicity absorption-selected galaxies at $z approx 0.5-0.8$ appear distinct from populations of star-forming galaxies at both $z approx 1.3-2.5$, during the peak of star formation activity in the Universe, and lower redshifts, $z lesssim 0.05$. Their relatively low SFRs, despite the large molecular gas reservoirs, may indicate a transition in the nature of star formation at intermediate redshifts, $z approx 0.7$.
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