The diffuse interstellar bands are absorption lines seen towards reddened stars(1). None of the molecules responsible for these bands have been conclusively identified(2). Two bands at 9,632 (a) over circle ngstroms and 9,577 (a) over circle ngstroms were reported in 1994, and were suggested to arise from C-60(+) molecules (ref. 3), on the basis of the proximity of these wavelengths to the absorption bands of C-60(+) measured in a neon matrix(4). Confirmation of this assignment requires the gas-phase spectrum of C-60(+). Here we report laboratory spectroscopy of C-60(+) in the gas phase, cooled to 5.8 kelvin. The absorption spectrum hasmaxima at 9,632.7 +/- 0.1 (a) over circle ngstroms and 9,577.5 +/- 0.1 (a) over circle ngstroms, and the full widths at half-maximum of these bands are 2.2 +/- 0.2 (a) over circle ngstroms and 2.5 +/- 0.2 (a) over circle ngstroms, respectively. We conclude that we have positively identified the diffuse interstellar bands at 9,632 (a) over circle ngstroms and 9,577 (a) over circle ngstroms as arising from C-60(+) in the interstellarmedium.