  Almost every helium atom in the Universe was created just a few minutes after
the Big Bang through a process commonly referred to as Big Bang
Nucleosynthesis. The amount of helium that was made during Big Bang
Nucleosynthesis is determined by the combination of particle physics and
cosmology. The current leading measures of the primordial helium abundance
(Y_P) are based on the relative strengths of H I and He I emission lines
emanating from star-forming regions in local metal-poor galaxies. As the
statistical errors on these measurements improve, it is essential to test for
systematics by developing independent techniques. Here we report the first
determination of the primordial helium abundance based on a near-pristine
intergalactic gas cloud that is seen in absorption against the light of a
background quasar. This gas cloud, observed when the Universe was just
one-third of its present age (z_abs = 1.724), has a metal content ~100 times
less than the Sun, and ~30 per cent less metals than the most metal-poor H II
region currently known where a determination of the primordial helium abundance
is afforded. We conclude that the helium abundance of this intergalactic gas
cloud is Y = 0.250^{+0.033}_{-0.025}, which agrees with the Standard Model
primordial value, Y_P = 0.24672 +/- 0.00017. Our determination of the
primordial helium abundance is not yet as precise as that derived using
metal-poor galaxies, but our method has the potential to offer a competitive
test of physics beyond the Standard Model during Big Bang Nucleosynthesis.
