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 _ { Mol } \approx ( 0.6 - 8.2 ) \times 10 ^ { 10 } \ > { M } _ { \odot } and high molecular gas fractions ( f _ { Mol } \equiv \ > M _ { Mol } / ( M _ { \ast } + M _ { Mol } ) \approx 0.29 - 0.87 ) . Their modest star formation rates ( SFRs ) , \approx ( 0.3 - 9.5 ) \ > { 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 .