We report the detection of a faint optical flash by the 2-m Faulkes Telescope North simultaneously with the second of two prompt gamma-ray pulses in INTEGRAL gamma-ray burst (GRB) 080603A, beginning at t_rest = 37 s after the onset of the GRB. This optical flash appears to be distinct from the subsequent emerging afterglow emission, for which we present comprehensive broadband radio to X-ray light curves to 13 days post-burst and rigorously test the standard fireball model. The intrinsic extinction toward GRB 080603A is high (A_V,z = 0.8 mag), and the well-sampled X-ray-to-near-infrared spectral energy distribution is interesting in requiring an LMC2 extinction profile, in contrast to the majority of GRBs. Comparison of the gamma-ray and extinction-corrected optical flux densities of the flash rules out an inverse-Compton origin for the prompt gamma-rays; instead, we suggest that the optical flash could originate from the inhomogeneity of the relativistic flow. In this scenario, a large velocity irregularity in the flow produces the prompt gamma-rays, followed by a milder internal shock at a larger radius that would cause the optical flash. Flat gamma-ray spectra, roughly F propto nu^-0.1, are observed in many GRBs. If the flat spectrum extends down to the optical band in GRB 080603A, the optical flare could be explained as the low-energy tail of the gamma-ray emission. If this is indeed the case, it provides an important clue to understanding the nature of the emission process in the prompt phase of GRBs and highlights the importance of deep (R> 20 mag), rapid follow-up observations capable of detecting faint, prompt optical emission.
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