  Primordial abundances of light elements are sensitive to the physics of the
early Universe and can directly constrain cosmological quantities, such as the
baryon-to-photon ratio $\eta_{10}$, the baryon density and the number of
neutrino families. Deuterium is especially suited for these studies: its
primordial abundance is sensitive and monotonically dependent on $\eta_{10}$,
allowing an independent measurement of the cosmic baryon density that can be
compared, for instance, against the Planck satellite data. The primordial
deuterium abundance can be measured in high $H_I$ column density absorption
systems towards distant quasars. We report here a new measurement, based on
high-resolution ESPRESSO data, of the primordial $D_I$ abundance of a system at
redshift $z \sim 3.572$, towards PKS1937-101. Using only ESPRESSO data, we find
a D/H ratio of $2.638\pm0.128 \times 10^{-5}$, while including the available
UVES data improves the precision, leading to a ratio of $2.608 \pm 0.102 \times
10^{-5}$. The results of this analysis agree with those of the most precise
existing measurements. We find that the relatively low column density of this
system ($\log{N_{\rm H_I}/ {\rm cm}^{-2}}\sim18 $) introduces modelling
uncertainties, which become the main contributor to the error budget.
