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 suggested(5,6). Carbon-based molecules ubiquitous in the interstellar medium have been widely favoured as potential carriers of some of the diffuse interstellar bands(7-10,29); in particular, C-60(+) has been thought to be a promising candidate(9,29). Here we present the results of a search for C-60(+) in the near-infrared spectra of seven stars, based on recent laboratory measurements of the absorption spectrum of this species(11-13). We find two diffuse bands that are coincident (within 0.1%) with laboratory measurements on C-60(+) in a Ne matrix(11). From this observation and the total absorption, we estimate that 0.3-0.9% of interstellar carbon is in the form of C-60(+). The molecule is very stable, which should allow it to survive in the interstellar medium for a long time(14), but the inhibition of C-60 formation by hydrogen probably limits its abundance.