  We report spectroscopic redshift measurements for three bright submillimeter
galaxies (SMGs) in the GOODS-N field, each with SCUBA-2 850 micron fluxes > 10
mJy, using the Northern Extended Millimeter Array (NOEMA). Our molecular
linescan observations of these sources, which occupy a ~7 arcmin$^2$ area
outside of the HST/ACS region of the field, reveal that two lie at $z \sim$
3.14 and thus likely belong to a previously-unknown overdensity of rare
galaxies, which we shall refer to as a protocluster. In the remaining object,
which is the brightest SCUBA-2 source in the entire GOODS-N, we detect line
emission consistent with CO(7-6), [C I], and H2O at $z$ = 4.42. The
far-infrared spectral energy distributions of these galaxies, constrained by
SCUBA-2, NOEMA, and Herschel/SPIRE, indicate instantaneous SFRs $\sim4000 ~{\rm
M_{\odot}~yr^{-1}}$ in the $z$ = 4.42 galaxy and $\sim 2500~{\rm
M_{\odot}~yr^{-1}}$ in the two $z \sim$ 3 galaxies. These occupy a co-moving
volume ~30 Mpc$^3$, making the protocluster one of the most compact,
spectroscopically-confirmed episodes of simultaneous dusty starbursts. Based on
our sources' CO line luminosities, we estimate $M_{{\rm gas}}\sim10^{11}
M_{\odot}$ and find gas depletion timescales of $\tau_{{\rm depl}}\sim 50$ Myr,
consistent with findings in other high-redshift SMG protoclusters.
