Gas clouds in present-day galaxies are inefficient at forming stars. Low star-formation efficiency is a critical parameter in galaxy evolution: it is why stars are still forming nearly 14 billion years after the Big Bang and why star clusters generally do not survive their births, instead dispersing to form galactic disks or bulges. Yet the existence of ancient massive bound star clusters (globular clusters) in the Milky Way suggests that efficiencies were higher when they formed ten billion years ago. A local dwarf galaxy, NGC 5253, has a young star cluster that provides an example of highly efficient star formation. Here we report the detection of the J = 3→2 rotational transition of CO at the location of the massive cluster. The gas cloud is hot, dense, quiescent and extremely dusty. Its gas-to-dust ratio is lower than the Galactic value, which we attribute to dust enrichment by the embedded star cluster. Its star-formation efficiency exceeds 50 per cent, tenfold that of clouds in the Milky Way. We suggest that high efficiency results from the force-feeding of star formation by a streamer of gas falling into the galaxy.