The relatively constant rate of star formation in galaxies like the Milky Way implies the need for continuum accretion of fresh gas. I present evidence that this accretion comes from the cooling of the virial-temperature coronae, that are thought to surround galaxy disks. This cooling is triggered by the passage of high-metallicity gas clouds ejected from the disks by supernovae. The prediction of this model is compared to neutral hydrogen observations of some local galaxies and the Milky Way. The gas accretion rates required to reproduce the data are about 1 M_Sun/yr, remarkably close to the star formation rates in these galaxies.