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 \sim 350 nearby ( D _ { L } \simeq 100 - 200 Mpc ) , massive galaxies ( \log ( M _ { \ast } / M _ { \odot } ) > 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 - 10 L ^ { \ast } 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 M _ { H 2 } / M _ { \ast } of the CO detections is 0.066 \pm 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 M _ { H 2 } / M _ { \ast } = 0.0016 \pm 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 .