We present the Combined Array for Research in Millimeter Astronomy (CARMA) ATLAS3D molecular gas imaging survey, a systematic study of the distribution and kinematics of molecular gas in CO-rich early-type galaxies. Our full sample of 40 galaxies (30 newly mapped and 10 taken from the literature) is complete to a 12CO(1-0) integrated flux of 18.5 Jy km s-1 and it represents the largest, best studied sample of its type to date. A comparison of the CO distribution of each galaxy to the g - r colour image (representing dust) shows that the molecular gas and dust distributions are in good agreement and trace the same underlying interstellar medium. The galaxies exhibit a variety of CO morphologies, including discs (50 per cent), rings (15 per cent), bars+rings (10 per cent), spiral arms (5 per cent) and mildly (12.5 per cent) and strongly (7.5 per cent) disrupted morphologies. There appear to be weak trends between galaxy mass and CO morphology, whereby the most massive galaxies in the sample tend to have molecular gas in a disc morphology. We derive a lower limit to the total accreted molecular gas mass across the sample of 2.48 × 1010 M⊙, or approximately 8.3 × 108 M⊙ per minor merger within the sample, consistent with minor merger stellar mass ratios.