We present extensive radio and millimeter observations of the unusually bright GRB 130427A at z=0.340, spanning 0.67 to 12 days after the burst. Taken in conjunction with detailed multi-band UV, optical, NIR, and X-ray observations we find that the broad-band afterglow emission is composed of distinct reverse shock and forward shock contributions. The reverse shock emission dominates in the radio/millimeter and at <0.1 days in the UV/optical/NIR, while the forward shock emission dominates in the X-rays and at >0.1 days in the UV/optical/NIR. We further find that the optical and X-ray data require a Wind circumburst environment, pointing to a massive star progenitor. Using the combined forward and reverse shock emission we find that the parameters of the burst are an isotropic kinetic energy of E_Kiso~2e53 erg, a mass loss rate of Mdot~3e-8 Msun/yr (for a wind velocity of 1,000 km/s), and a Lorentz factor at the deceleration time of Gamma(200s)~130. Due to the low density and large isotropic energy, the absence of a jet break to ~15 days places only a weak constraint on the opening angle of theta_j>2.5 deg, and therefore a total energy of E_gamma+E_K>1.2e51 erg, similar to other GRBs. The reverse shock emission is detectable in this burst due to the low circumburst density, which leads to a slow cooling shock. We speculate that this is a required property for the detectability of reverse shocks in the radio and millimeter bands. Following on GRB 130427A as a benchmark event, observations of future GRBs with the exquisite sensitivity of VLA and ALMA, coupled with detailed modeling of the reverse and forward shock contributions will test this hypothesis.
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