  In the early Universe finding massive galaxies that have stopped forming
stars present an observational challenge as their rest-frame ultraviolet
emission is negligible and they can only be reliably identified by extremely
deep near-infrared surveys. These have revealed the presence of massive,
quiescent early-type galaxies appearing in the universe as early as z$\sim$2,
an epoch 3 Gyr after the Big Bang. Their age and formation processes have now
been explained by an improved generation of galaxy formation models where they
form rapidly at z$\sim$3-4, consistent with the typical masses and ages derived
from their observations. Deeper surveys have now reported evidence for
populations of massive, quiescent galaxies at even higher redshifts and earlier
times, however the evidence for their existence, and redshift, has relied
entirely on coarsely sampled photometry. These early massive, quiescent
galaxies are not predicted by the latest generation of theoretical models.
Here, we report the spectroscopic confirmation of one of these galaxies at
redshift z=3.717 with a stellar mass of 1.7$\times$10$^{11}$ M$_\odot$ whose
absorption line spectrum shows no current star-formation and which has a
derived age of nearly half the age of the Universe at this redshift. The
observations demonstrates that the galaxy must have quickly formed the majority
of its stars within the first billion years of cosmic history in an extreme and
short starburst. This ancestral event is similar to those starting to be found
by sub-mm wavelength surveys pointing to a possible connection between these
two populations. Early formation of such massive systems is likely to require
significant revisions to our picture of early galaxy assembly.
