We report the identification of radio (1.4 and 3 GHz) and mid-infrared, far-infrared, and sub-mm (24-850$mu$m) emission at the position of one of 41 UV-bright ($mathrm{M_{UV}^{}}lesssim-21.25$) $zsimeq6.6-6.9$ Lyman-break galaxy candidates in the 1.5 deg$^2$ COSMOS field. This source, COS-87259, exhibits a sharp flux discontinuity (factor $>$3) between two narrow/intermediate bands at 9450 $mathring{A}$ and 9700 $mathring{A}$ and is undetected in all nine bands blueward of 9600 $mathring{A}$, as expected from a Lyman-alpha break at $zsimeq6.8$. The full multi-wavelength (X-ray through radio) data of COS-87529 can be self-consistently explained by a very massive (M$_{ast}=10^{10.8}$ M$_{odot}$) and extremely red (rest-UV slope $beta=-0.59$) $zsimeq6.8$ galaxy with hyperluminous infrared emission (L$_{mathrm{IR}}=10^{13.6}$ L$_{odot}$) powered by both an intense burst of highly-obscured star formation (SFR$approx$1800 M$_{odot}$ yr$^{-1}$) and an obscured ($tau_{mathrm{9.7mu m}}=7.7pm2.5$) radio-loud (L$_{mathrm{1.4 GHz}}sim10^{25.5}$ W Hz$^{-1}$) AGN. The radio emission is compact (1.04$pm$0.12 arcsec) and exhibits an ultra-steep spectrum between 1.4-3 GHz ($alpha=-2.06^{+0.27}_{-0.25}$) with evidence of spectral flattening at lower frequencies, consistent with known $z>4$ radio galaxies. We also demonstrate that COS-87259 may reside in a significant (11$times$) galaxy overdensity at $zsimeq6.6-6.9$, as common for systems hosting radio-loud AGN. Nonetheless, a spectroscopic redshift will ultimately be required to establish the true nature of COS-87259 as we cannot yet completely rule out low-redshift solutions. If confirmed to lie at $zsimeq6.8$, the properties of COS-87259 would be consistent with a picture wherein AGN and highly-obscured star formation activity are fairly common among very massive (M$_{ast}>10^{10}$ M$_{odot}$) reionization-era galaxies.
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