We present multi-wavelength observations and modeling of the exceptionally bright long $gamma$-ray burst GRB 160625B. The optical and X-ray data are well-fit by synchrotron emission from a collimated blastwave with an opening angle of $theta_japprox 3.6^circ$ and kinetic energy of $E_Kapprox 2times10^{51}$ erg, propagating into a low density ($napprox 5times10^{-5}$ cm$^{-3}$) medium with a uniform profile. The forward shock is sub-dominant in the radio band; instead, the radio emission is dominated by two additional components. The first component is consistent with emission from a reverse shock, indicating an initial Lorentz factor of $Gamma_0gtrsim 100$ and an ejecta magnetization of $R_Bapprox 1-100$. The second component exhibits peculiar spectral and temporal evolution and is most likely the result of scattering of the radio emission by the turbulent Milky Way interstellar medium (ISM). Such scattering is expected in any sufficiently compact extragalactic source and has been seen in GRBs before, but the large amplitude and long duration of the variability seen here are qualitatively more similar to extreme scattering events previously observed in quasars, rather than normal interstellar scintillation effects. High-cadence, broadband radio observations of future GRBs are needed to fully characterize such effects, which can sensitively probe the properties of the ISM and must be taken into account before variability intrinsic to the GRB can be interpreted correctly.
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