Understanding stellar birth requires observations of the clouds in which they form. These clouds are dense and self-gravitating, and in all existing observations they are molecular, with H-2 the dominant species and carbon monoxide (CO) the best available tracer(1,2). When the abundances of carbon and oxygen are low compared with that of hydrogen, and the opacity from dust is also low, as in primeval galaxies and local dwarf irregular galaxies(3), CO forms slowly and is easily destroyed, so it is difficult for it to accumulate inside dense clouds(4). Here we report interferometric observations of CO clouds in the local group dwarf irregular galaxy Wolf-Lundmark-Melotte (WLM)(5), which has a metallicity that is 13 per cent of the solar value(6,7) and 50 per cent lower than the previous CO detection threshold. The clouds are tiny compared to the surrounding atomic and H-2 envelopes, but they have typical densities and column densities for CO clouds in the Milky Way. The normal CO density explains why star clusters forming in dwarf irregulars have similar densities to star clusters in giant spiral galaxies. The low cloud masses suggest that these clusters will also be low mass, unless some galaxy-scale compression occurs, such as an impact from a cosmic cloud or other galaxy. If the massive metal-poor globular clusters in the halo of the Milky Way formed in dwarf galaxies, as is commonly believed, then they were probably triggered by such an impact.