  We present Very Large Array (VLA) and Atacama Large Millimeter/sub-millimeter
Array ALMA radio observations of GW\,170817, the first Laser Interferometer
Gravitational-wave Observatory (LIGO)/Virgo gravitational wave (GW) event from
a binary neutron star merger and the first GW event with an electromagnetic
(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 and 39.23 days 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 to 30 days post merger, ruling out an on-axis short gamma-ray burst (SGRB)
for energies $\gtrsim 10^{48}$ erg. For fiducial SGRB parameters, our limits
require an observer viewer angle of $\gtrsim 20^{\circ}$. The radio and X-ray
data can be jointly explained as the afterglow emission from an SGRB with a jet
energy of $\sim 10^{49}-10^{50}$ erg that exploded in a uniform density
environment with $n\sim 10^{-4}-10^{-2}$ cm$^{-3}$, viewed at an angle of $\sim
20^{\circ}-40^{\circ}$ 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 (KN) ejecta on a timescale of $\sim 5-10$ years
that will remain detectable for decades with next-generation radio facilities,
making GW\,170817 a compelling target for long-term radio monitoring.
