The formation of planets around binary stars may be more difficult than around single stars1, 2, 3. In a close binary star(with a separation of less than a hundred astronomical units), theory predicts the presence of circumstellar disks aroundeach star, and an outer circumbinary disk surrounding a gravitationally cleared inner cavity around the stars4, 5. Given thatthe inner disks are depleted by accretion onto the stars on timescales of a few thousand years, any replenishing materialmust be transferred from the outer reservoir to fuel planet formation (which occurs on timescales of about one millionyears). Gas flowing through disk cavities has been detected in single star systems6. A circumbinary disk was discoveredaround the young low-mass binary system GG Tau A (ref. 7), which has recently been shown to be a hierarchical triplesystem8. It has one large inner disk9 around the single star, GG Tau Aa, and shows small amounts of shocked hydrogengas residing within the central cavity10, but other than a single weak detection11, the distribution of cold gas in this cavityor in any other binary or multiple star system has not hitherto been determined. Here we report imaging of gas fragmentsemitting radiation characteristic of carbon monoxide within the GG Tau A cavity. From the kinematics we conclude that theflow appears capable of sustaining the inner disk (around GG Tau Aa) beyond the accretion lifetime, leaving time for planetformation to occur there. These results show the complexity of planet formation around multiple stars and confirm thegeneral picture predicted by numerical simulations.< Réduire