Binary neutron-star mergers (BNSMs) are among the most readily detectable gravitational-wave (GW) sources with LIGO. They are also thought to produce short $gamma$-ray bursts (SGRBs), and kilonovae that are powered by r-process nuclei. Detecting these phenomena simultaneously would provide an unprecedented view of the physics during and after the merger of two compact objects. Such a Rosetta Stone event was detected by LIGO/Virgo on 17 August 2017 at a distance of $sim 44$ Mpc. We monitored the position of the BNSM with ALMA at 338.5 GHz and GMRT at 1.4 GHz, from 1.4 to 44 days after the merger. Our observations rule out any afterglow more luminous than $3times 10^{26}~{rm erg,s}^{-1},{rm Hz}^{-1}$ in these bands, probing $>$2--4 dex fainter than previous SGRB limits. We match these limits, in conjunction with public data announcing the appearance of X-ray and radio emission in the weeks after the GW event, to templates of off-axis afterglows. Our broadband modeling suggests that GW170817 was accompanied by a SGRB and that the GRB jet, powered by $E_{rm AG,,iso}sim10^{50}$~erg, had a half-opening angle of $sim20^circ$, and was misaligned by $sim41^circ$ from our line of sight. The data are also consistent with a more collimated jet: $E_{rm AG,,iso}sim10^{51}$~erg, $theta_{1/2,,rm jet}sim5^circ$, $theta_{rm obs}sim17^circ$. This is the most conclusive detection of an off-axis GRB afterglow and the first associated with a BNSM-GW event to date. Assuming a uniform top-hat jet, we use the viewing angle estimates to infer the initial bulk Lorentz factor and true energy release of the burst.
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