We present observations with the IRAM 30 m telescope of CO in a large sample of ultraluminous IR galaxies out to redshift z = 0.3. Most of the ultraluminous galaxies in this sample are interacting, but not completed, mergers. The CO(1-0) luminosity of all but one of the ultraluminous galaxies is high, with values of log (L/K km s^-1 pc²) = 9.92 ± 0.12. The extremely small dispersion of only 30% is less than that of the far-infrared luminosity. The integrated CO line intensity is strongly correlated with the 100 μm flux density, as expected for a blackbody model in which the mid- and far-IR radiation is optically thick. We use this model to derive sizes of the FIR- and CO-emitting regions and the enclosed dynamical masses. Both the IR and CO emission originate in regions a few hundred parsecs in radius. The median value of L_FIR/L=160 L/K km s^-1 pc², within a factor of 2 or 3 of the blackbody limit for the observed far-IR temperatures. The entire ISM is a scaled-up version of a normal galactic disk with the ambient densities a factor of 100 higher, making even the intercloud medium a molecular region. We compare three different techniques of H₂ mass estimation and conclude that the ratio of gas mass to CO luminosity is about a factor of 4 times lower than for giant molecular clouds (GMCs) but that the gas mass is a large fraction of the dynamical mass. Our analysis of CO emission from ultraluminous galaxies reduces the H₂ mass from previous estimates of 2-5 × 10¹⁰ M to 0.4-1.5 × 10¹⁰ M, which is in the range found for molecular gas-rich spiral galaxies. A collision involving a molecular gas-rich spiral could lead to an ultraluminous galaxy powered by central starbursts triggered by the compression of infalling preexisting GMCs.

The extremely dense molecular gas in the center of an ultraluminous galaxy is an ideal stellar nursery for a huge starburst.