  We are conducting COLD GASS, a legacy survey for molecular gas in nearby
galaxies. Using the IRAM 30m telescope, we measure the CO(1-0) line in a sample
of ~350 nearby (D=100-200 Mpc), massive galaxies (log(M*/Msun)>10.0). The
sample is selected purely according to stellar mass, and therefore provides an
unbiased view of molecular gas in these systems. By combining the IRAM data
with SDSS photometry and spectroscopy, GALEX imaging and high-quality Arecibo
HI data, we investigate the partition of condensed baryons between stars,
atomic gas and molecular gas in 0.1-10L* galaxies. In this paper, we present CO
luminosities and molecular hydrogen masses for the first 222 galaxies. The
overall CO detection rate is 54%, but our survey also uncovers the existence of
sharp thresholds in galaxy structural parameters such as stellar mass surface
density and concentration index, below which all galaxies have a measurable
cold gas component but above which the detection rate of the CO line drops
suddenly. The mean molecular gas fraction MH2/M* of the CO detections is
0.066+/-0.039, and this fraction does not depend on stellar mass, but is a
strong function of NUV-r colour. Through stacking, we set a firm upper limit of
MH2/M*=0.0016+/-0.0005 for red galaxies with NUV-r>5.0. The average
molecular-to-atomic hydrogen ratio in present-day galaxies is 0.3, with
significant scatter from one galaxy to the next. The existence of strong
detection thresholds in both the HI and CO lines suggests that "quenching"
processes have occurred in these systems. Intriguingly, atomic gas strongly
dominates in the minority of galaxies with significant cold gas that lie above
these thresholds. This suggests that some re-accretion of gas may still be
possible following the quenching event.
