Puzzlingly, the parent bodies of ordinary chondrites (the most abundant type of meteorites) do not seem to be abundant among asteroids. One possible explanation is that surfaces of the parent bodies become optically altered, to become the S-type asteroids which are abundant in the main asteroid belt. The process is called 'space weathering'-it makes the visible and near-infrared reflectance spectrum of a body darker and redder. A recent survey of small, near-Earth asteroids suggests that the surfaces of small S asteroids may have developing stages of space weathering. Here we report that a dark region on a small (550-metre) asteroid-25143 Itokawa-is significantly more space-weathered than a nearby bright region. Spectra of both regions are consistent with those of LL5-6 chondrites after continuum removal. A simple calculation suggests that the dark area has a shorter mean optical path length and about 0.04 per cent by volume more nanophase metallic iron particles than the bright area. This clearly shows that space-weathered materials accumulate on small asteroids, which are likely to be the parent bodies of LL chondrites. We conclude that, because LL meteorites are the least abundant of ordinary (H, L, and LL) chondrites, there must be many asteroids with ordinary-chondrite compositions in near-Earth orbits.