Carbon monoxide (CO) is the primary tracer for interstellar clouds where stars form, but it has never been detected in galaxies in which the oxygen abundance relative to hydrogen is less than 20 per cent of that of the Sun, even though such `low-metallicity' galaxies often form stars. This raises the question of whether stars can form in dense gas without molecules, cooling to the required near-zero temperatures by atomic transitions and dust radiation rather than by molecular line emission; and it highlights uncertainties about star formation in the early Universe, when the metallicity was generally low. Here we report the detection of CO in two regions of a local dwarf irregular galaxy, WLM, where the metallicity is 13 per cent of the solar value. We use new submillimetre observations and archival far-infrared observations to estimate the cloud masses, which are both slightly greater than 100,000 solar masses. The clouds have produced stars at a rate per molecule equal to 10 per cent of that in the local Orion nebula cloud. The CO fraction of the molecular gas is also low, about 3 per cent of the Milky Way value. These results suggest that in small galaxies both star-forming cores and CO molecules become increasingly rare in molecular hydrogen clouds as the metallicity decreases.