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Optical and near-infrared observations of the gamma-ray burst GRB 031203, at z= 0.1055, are reported. A very faint afterglow is detected superposed onto the host galaxy in our first infrared JHK observations, carried out~ 9 hr after the burst. Subsequently, a rebrightening is detected in all bands, peaking in the R band about 18 rest-frame days after the burst. The rebrightening closely resembles the light curve of a supernova like SN 1998bw, assuming that the GRB and the SN went off almost simultaneously, but with a somewhat slower evolution. Spectra taken close to the maximum of the rebrightening show extremely broad features as in SN 1998bw. The determination of the absolute magnitude of this SN (SN 2003lw) is difficult owing to the large and uncertain extinction, but likely this event was brighter than SN 1998bw by 0.5 mag in the VRI bands, reaching an absolute magnitude M V=-19.75±0.15.