The Telescope a Action Rapide pour les Objets Transitoires (TAROT-1) has as its prime objective the observation of the prompt and delayed emission of cosmic gamma-ray bursts (GRBs). We have performed a search for optical emission from 6 GRBs detected by BATSE. The positioning error circle was fully covered within typically thirty minutes after the trigger. No detection of the early afterglow phase was made, and magnitude limits in the range of m(R) = 13-15 were estimated using 20 s exposures. These limits are compared to optical afterglow data obtained in later phases and the results are interpreted in terms of source distances. They correspond to a median redshift of z = 0.5. With HETE-2 and the planned instrument upgrade, TAROT-1 will be able to detect the early optical emission of GRBs up to a redshift of the order of 5.