  Stars form from cold molecular interstellar gas. Since this is relatively
rare in the local Universe, galaxies like the Milky Way form only a few new
stars per year. Typical massive galaxies in the distant Universe formed stars
an order of magnitude more rapidly. Unless star formation was significantly
more efficient, this difference suggests that young galaxies were much more gas
rich. Molecular gas observations in the distant Universe have so far been
largely restricted to very luminous, rare objects, including mergers and
quasars. Here we report the results of a systematic survey of molecular gas in
samples of typical massive star forming galaxies at <z>~1.2 and 2.3, when the
Universe was 40% and 24% of its current age. Our measurements provide empirical
evidence that distant star forming galaxies indeed were gas rich, and that the
star formation efficiency is not strongly dependent on cosmic epoch. The
average fraction of cold gas relative to total galaxy baryonic mass at z= 2.3
and z=1.2 is ~44% and 34%, three to ten times higher than in today's massive
spiral galaxies. The slow decrease between z~2 and 1 probably requires a
mechanism of semi-continuous replenishment of fresh gas to the young galaxies.
