An optical transient within the error box of the gamma ray burst GRB 970508 was imaged 4 hours after the event. It displayed a strong ultraviolet excess, and reached maximum brightness 2 days later. The optical spectra did not show any emission lines, and no variations on time scales of minutes were observed for 1 hour during the decline phase. According to the fireball and afterglow models, the intensity should rise monotonically before the observed optical maximum, but the data indicate that another physical mechanism may be responsible for the constant phase seen during the first hours after the burst.