We report on observations of a gamma-ray burst (GRB 061126) with an extremely bright (R ≈ 12 mag at peak) early-time optical afterglow. The optical afterglow is already fading as a power law 22 s after the trigger, with no detectable prompt contribution in our first exposure, which was coincident with a large prompt-emission gamma-ray pulse. The optical- infrared photometric SED is an excellent fit to a power law, but it exhibits a moderate red-to-blue evolution in the spectral index at about 500 s after the burst. This color change is contemporaneous with a switch from a relatively fast decay to slower decay. The rapidly decaying early afterglow is broadly consistent with synchrotron emission from a reverse shock, but a bright forward-shock component predicted by the intermediate- to late-time X-ray observations under the assumptions of standard afterglow models is not observed. Indeed, despite its remarkable early-time brightness, this burst would qualify as a dark burst at later times on the basis of its nearly flat optical-to-X-ray spectral index. Our photometric SED provides no evidence of host galaxy extinction, requiring either large quantities of gray dust in the host system (at redshift 1.1588 +/- 0.0006, based on our late-time Keck spectroscopy) or separate physical origins for the X-ray and optical afterglows.