The gas accretion and star-formation histories of galaxies like the Milky Way remain an outstanding problem in astrophysics. Observations show that 8 billion years ago, the progenitors to Milky Way-mass galaxies were forming stars 30 times faster than today and predicted to be rich in molecular gas, in contrast with low present-day gas fractions ($<$10%). Here we show detections of molecular gas from the CO(J=3-2) emission (rest-frame 345.8 GHz) in galaxies at redshifts z=1.2-1.3, selected to have the stellar mass and star-formation rate of the progenitors of todays Milky Way-mass galaxies. The CO emission reveals large molecular gas masses, comparable to or exceeding the galaxy stellar masses, and implying most of the baryons are in cold gas, not stars. The galaxies total luminosities from star formation and CO luminosities yield long gas-consumption timescales. Compared to local spiral galaxies, the star-formation efficiency, estimated from the ratio of total IR luminosity to CO emission,} has remained nearly constant since redshift z=1.2, despite the order of magnitude decrease in gas fraction, consistent with results for other galaxies at this epoch. Therefore the physical processes that determine the rate at which gas cools to form stars in distant galaxies appear to be similar to that in local galaxies.
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