We report measurements of, and upper limits for, millimeter-wavelength CO emission from interstellar clouds which have previously been studied via optical absorption lines. Along with CO measurements made by the Copernicus satellite, the results can be used to place constraints on models for interstellar chemistry. Our results are roughly consistent with models in which CO is produced by gas-phase reactions, and we find evidence to support calculations that a necessary but not sufficient condition for detecting the millimeter-wavelength CO lines is that the total gas density be greater than about 1000 cm/sup -3/. Some of the clouds we have observed appear to be nearly self-gravitating and may therefore be in the very first stages of star formation. (AIP)