The discovery of afterglows associated with γ-ray bursts at X-ray, optical and radio wavelengths and the measurement of the redshifts of some of these events, has established that γ-ray bursts lie at extreme distances, making them the most powerful photon-emitters known in the Universe. Here we report the discovery of transient optical emission in the error box of the γ-ray burst GRB980425, the light curve of which was very different from that of previous optical afterglows associated with γ-ray bursts. The optical transient is located in a spiral arm of the galaxy ESO184-G82, which has a redshift velocity of only 2,550kms-1 (ref. 6). Its optical spectrum and location indicate that it is a very luminous supernova, which has been identified as SN1998bw. If this supernova and GRB980425 are indeed associated, the energy radiated in γ-rays is at least four orders of magnitude less than in other γ-ray bursts, although its appearance was otherwise unremarkable: this indicates that very different mechanisms can give rise to γ-ray bursts. But independent of this association, the supernova is itself unusual, exhibiting an unusual light curve at radio wavelengths that requires that the gas emitting the radio photons be expanding relativistically,.