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.
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