The gas accretion and star formation histories of galaxies like the Milky Way remain an outstanding problem in astrophysics ^1,2 . Observations show that 8 billion years ago, the progenitors to Milky Way-mass galaxies were forming stars 30 times faster than today and were predicted to be rich in molecular gas ³ , in contrast to the low present-day gas fractions (<10%) ^4-6 . Here we show the detection 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 today's Milky Way-mass galaxies. The CO emission reveals large molecular gas masses, comparable to or exceeding the galaxy stellar masses, and implying that most of the baryons are in cold gas, not stars. The total luminosities of the galaxies 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 infrared luminosity (L _IR) to CO emission, has remained nearly constant since redshift z = 1.2, despite the order of magnitude decrease in gas fraction, consistent with the results for other galaxies at this epoch ^7-10 . 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.