MORE than a hundred well-defined absorption bands, arising from diffuse gas in the interstellar medium, have been observed in the visible and near-infrared spectra of stars 1-4. The identity of the species responsible for these bands has remained unclear, although many possibilities have been suggested5,6. Carbon-based molecules ubiquitous in the interstellar medium have been widely favoured as potential carriers of some of the diffuse interstellar bands7-10,29 in particular, C60+ has been thought to be a promising candidate9,29. Here we present the results of a search for C60+ in the near-infrared spectra of seven stars, based on recent laboratory measurements of the absorption spectrum of this species11-13. We find two diffuse bands that are coincident (within 0.1%) with laboratory measurements on C60+ in a Ne matrix11. From this observation and the total absorption, we estimate that 0.3-0.9% of interstellar carbon is in the form of C60+. The molecule is very stable, which should allow it to survive in the interstellar medium for a long time14, but the inhibition of C60+ formation by hydrogen probably limits its abundance.