We present a multiwavelength analysis of Swift GRB 061007. The 2-m robotic Faulkes Telescope South (FTS) began observing 137 s after the onset of the gamma-ray emission, when the optical counterpart was already decaying from R 10.3 mag, and continued observing for the next 5.5 hours. These observations begin during the final gamma-ray flare and continue through and beyond a long, soft tail of gamma-ray emission whose flux shows an underlying simple power-law decay identical to that seen at optical and X-ray wavelengths, with temporal slope alpha 1.7 This remarkably simple decay in all of these bands is rare for Swift bursts, which often show much more complex light curves. We suggest the afterglow emission begins as early as 30-100 s and is contemporaneous with the on-going variable prompt emission from the central engine, but originates from a physically distinct region dominated by the forward shock. The afterglow continues unabated until at least 10^5 s showing no evidence of a break. The observed multiwavelength evolution of GRB 061007 is explained by an expanding fireball whose optical, X-ray and late-time gamma-ray emission is dominated by emission from a forward shock with typical synchrotron frequency, nu_m, that is already below the optical band as early as t=137 s and a cooling frequency, nu_c, above the X-ray band to at least t=10^5 s. In contrast, the typical frequency of the reverse shock lies in the radio band at early time. We suggest that the unexpected lack of bright optical flashes from the majority of Swift GRBs may be explained with a low nu_m originating from small microphysics parameters, epsilon_e and epsilon_B. (Abridged)
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