For almost a quarter of a century(1), the origin of gamma-ray bursts-brief, energetic bursts of high-energy photons-has remained unknown. The detection of a counterpart at another wavelength has long been thought to be a key to understanding the nature of these bursts (see, for example, ref. 2), but intensive searches have not revealed such a counterpart. The distribution and properties of the bursts(3) are explained naturally if they lie at cosmological distances (a few Gpc)(4), but there is a countervailing view that they are relatively local objects(5), perhaps distributed in a very large halo around our Galaxy. Here we report the detection of a transient and fading optical source in the error box associated with the burst GRB970228, less than 21 hours after the burst(6,7). The optical transient appears to be associated with a faint galaxy(7,8), suggesting that the burst occurred in that galaxy and thus that gamma-ray bursts in general lie at cosmological distance.