The ice-rich surface of the jovian satellite Europa is sparsely cratered, suggesting that this moon might be geologically active today. Moreover, models of the satellite's interior indicate that tidal interactions with Jupiter might produce enough heat to maintain a subsurface liquid water layer. But the mechanisms of interior heat loss and resurfacing are currently unclear, as is the question of whether Europa has (or had at one time) a liquid water ocean,. Here we report on the morphology and geological interpretation of distinct surface features-pits, domes and spots-discovered in high-resolution images of Europa obtained by the Galileo spacecraft. The features are interpreted as the surface manifestation of diapirs, relatively warm localized ice masses that have risen buoyantly through the subsurface. We find that the formation of the features can be explained by thermally induced solid-state convection within an ice shell, possibly overlying a liquid water layer. Our results are consistent with the possibility that Europa has a liquid water ocean beneath a surface layer of ice, but further tests and observations are needed to demonstrate this conclusively.