Searches for molecular line emission from high redshift galaxies have become one of the recent highlights in millimeter astronomy, largely because detection of this emission enables one to study the potential for star formation in galaxies at epochs close to galaxy formation. Such information is crucial to models of galaxy evolution. Thus far, most of the searches have been to try to detect any of the rotational lines of CO, although many authors have also inferred the presence of molecular gas through detections of cold dust in the submillimeter region of the spectrum. In addition to providing information about the physical properties of the molecular gas in distant galaxies (when more than one transition or isotope is detected), the CO lines can be used to place stringent constrints on the dynamical masses of these systems. Moreover, since millimeter data has spectral resolutions of typically a few tens of km/s, one can pin down the redshift of the host galaxy with extremely high precision. One of the driving forces in most of the searches for CO emission at high redshift is the fact that molecular gas is known to be an important constituent in the low redshift counterparts to the types of objects that one expects to find at high redshifts, the Ultraluminous Infrared Galaxies (ULIRGs), (e.g. Mirabel and Sanders 1985; Sanders et al. 1986), powerful radio galaxies (e.g. Mazzarella et al. 1993), and nearby quasars (e.g. Barvainis et al. 1989), for example.