We present VLA and ALMA radio observations of GW170817, the first LIGO/Virgo gravitational wave event from a binary neutron star merger and the first GW event with an EM counterpart. Our data include the first observations following the discovery of the optical transient at both the centimeter (13:7 hours post merger) and millimeter (2:41 days post merger) bands. We detect faint emission at 6 GHz at 19.47 d and 39.23 d after the merger, but not in an earlier observation at 2.46 d. We do not detect cm/mm emission at the position of the optical counterpart at frequencies of 10-97.5 GHz at times ranging from 0.6-30 d post merger, ruling out an on-axis short gamma-ray burst (SGRB) for energies & 1048 erg. For fiducial SGRB parameters, our limits require an observer viewer angle of >= 20 degrees. The radio and X-ray data can be jointly explained as the afterglow emission from a SGRB with a jet energy of ~ 10^49 - 10^50 erg that exploded in a uniform density environment with n ~ 10^-4 -10^-2 cm-3, viewed at an angle of ~ 20-40 degrees from the jet axis. Using the results of our light curve and spectral modeling, in conjunction with the inference of the circumbinary density, we predict the emergence of late-time radio emission from the deceleration of the kilonova ejecta on a timescale of ~ 5 - 10 yr that will remain detectable for decades with next generation radio facilities, making GW170817 a compelling target for long-term radio monitoring.