RICH clusters of galaxies contain more hot gas by mass than stars(1 3) . This gas is not associated with individual galaxies, but instead is smoothly distributed, like the dark matter that is inferred to reside in the clusters. Identifying the origin of this gas will allow us to constrain theories of galaxy formation by Placing limits on the efficiency with which gas is converted into stars and on the fraction of the cluster mass that is comprised of normal baryonic matter. Here me suggest that this gas was originally condensed into dwarf galaxies, precursors to the low-surface-brightness dwarf spheroidal galaxies now observed. The condensed gas would have fuelled a burst of star formation, leading to supernova-driven winds(4) which could have expelled the gas back into the intracluster-medium. We show that this model can easily account for most of the present X-ray-emitting cluster gas.