Past studies of cosmological gamma-ray bursts (GRBs) have been hampered by their extreme distances, resulting in faint afterglows. A nearby GRB could potentially shed much light on the origin of these events, but GRBs with a redshift z <or= 0.2 have been estimated to occur only rarely, about once per decade. Here we report the discovery of the bright optical afterglow emission from the burst of 29 March 2003 (GRB030329; ref. 2). The brightness of the afterglow and the prompt report of its position resulted in extensive follow-up observations at many wavelengths, along with the measurement of the redshift, z = 0.169 (ref. 4). The gamma-ray and afterglow properties of GRB030329 are similar to those of GRBs at cosmological redshifts. Observations have already identified the progenitor as a massive star that exploded as a supernova.