The Robotic Optical Transient Search Experiment (ROTSE) seeks to measure simultaneous and early afterglow optical emission from gamma-ray bursts (GRBs). A search for optical counterparts to six GRBs with localization errors of 1 square degree or better produced no detections. The earliest limiting sensitivity is m(ROTSE) > 13.1 at 10.85 seconds (5 second exposure) after the gamma-ray rise, and the best limit is m(ROTSE) > 16.0 at 62 minutes (897 second exposure). These are the most stringent limits obtained for GRB optical counterpart brightness in the first hour after the burst. Consideration of the gamma-ray fluence and peak flux for these bursts and for GRB990123 indicates that there is not a strong positive correlation between optical flux and gamma-ray emission.
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