The ROTSE-IIIc telescope at the HESS site, Namibia, obtained the earliest detection of optical emission from a gamma-ray burst (GRB), beginning only 21.8 s from the onset of Swift GRB 050801. The optical light curve does not fade or brighten significantly over the first 6250 s, after which there is an achromatic break and the light curve declines in typical power-law fashion. The Swift XRT also obtained early observations starting at 69 s after the burst onset. The X-ray light curve shows the same features as the optical light curve. These correlated variations in the early optical and X-ray emission imply a common origin in space and time. This behavior is difficult to reconcile with the standard models of early afterglow emission.