We propose a new interpretation for the CO-emitting region of the Cloverleaf (H1413+1143), a gravitationally lensed quasi-stellar object. We fitted a two-galaxy lensing model directly to the Institut de Radioastronomie Millimetrique CO (7-6) data rather than to the optical Hubble Space Telescope image, and from the fit we infer that the CO (7-6) source is a disklike structure with a characteristic radius of 785 pc,(1) a size similar to that of the CO-emitting regions present in nearby starburst ultraluminous infrared galaxies. We therefore suggest that the Cloverleaf contains both an extended rotating molecular starburst disk and a central quasar.