  We review the evolution of the cosmic average molecular gas density to large
look-back times, using observations of rotational transitions of CO. Molecular
gas is the fuel for star formation in galaxies. Deep searches for CO emission
from distant galaxies have delineated the density of molecular gas back to $z
\sim 5$, or within 1~Gyr of the Big Bang. The results show a rise and fall in
the gas density that parallels, and likely drives, the rise and fall of the
cosmic star formation rate density. We present the potential for the next
generation Very Large Array to image the distribution and dynamics of the
molecular gas in early galaxies, and to make a precise measurement of the dense
gas history of the Universe.
