It has been suggested that Earth's current supply of water was delivered by asteroids, some time after the collision that produced the Moon (which would have vaporized any of the pre-existing water). So far, no measurements of water ice on asteroids have been made, but its presence has been inferred from the comet-like activity of several small asteroids, including two members of the Themis dynamical family. Here we report infrared spectra of the asteroid 24 Themis which show that ice and organic compounds are not only present on its surface but also prevalent. Infrared spectral differences between it and other asteroids make 24 Themis unique so far, and our identification of ice and organics agrees with independent results that rule out other compounds as possible sources of the observed spectral structure. The widespread presence of surface ice on 24 Themis is somewhat unexpected because of the relatively short lifetime of exposed ice at this distance (~3.2AU) from the Sun. Nevertheless, there are several plausible sources, such as a subsurface reservoir that brings water to the surface through `impact gardening' and/or sublimation.