The J = 1–0 rotational transition of carbon monoxide has been used to trace the molecular gas at five different positions in the Circinus galaxy using the Australia Telescope National Facility's 22 m radio telescope at Mopra. The intensity profile of the central CO emission has a full width at half maximum of 550 pc. The 12CO (1–0) spectrum at the centre of the galaxy has an integrated temperature of 145 K km S−1, with components peaking at 0·62 K and ranging in velocity from 200–600 km S−1. The total mass of molecular gas in the Circinus galaxy, assuming that the CO intensity profile of the galaxy is similar to the radio continuum, is at least 7·5±4·1 × 108 M⊙. This estimate, combined with previously published far infrared data, yields a value for the star-forming efficiency, SFE = 16±9 L⊙ M⊙‒1.