  We present spectra of the most massive quiescent galaxy yet discovered at
$z>3$, spectroscopically confirmed via the detection of Balmer absorption
features in the $H-$ and $K-$bands of Keck/MOSFIRE. The spectra confirm a
galaxy with no significant ongoing star formation, consistent with the lack of
rest-frame UV flux and overall photometric spectral energy distribution. With a
stellar mass of $3.1^{+0.1}_{-0.2} \times 10^{11} ~\rm{M}_\odot$ at $z =
3.493$, this galaxy is nearly three times more massive than the highest
redshift spectroscopically confirmed absorption-line identified galaxy known.
The star-formation history of this quiescent galaxy implies that it formed
$>1000 ~\rm{M}_\odot$/yr for almost 0.5 Gyr beginning at $z\sim7.2$, strongly
suggestive that it is the descendant of massive dusty star-forming galaxies at
$5<z<7$ recently observed with ALMA. While galaxies with similarly extreme
stellar masses are reproduced in some simulations at early times, such a lack
of ongoing star formation is not seen there. This suggests the need for a more
rapid quenching process than is currently prescribed, challenging our current
understanding of how ultra-massive galaxies form and evolve in the early
Universe.
