  Chemical evolution models predict a gradual build-up of $^{13}$C in the
universe, based on empirical nuclear reaction rates and assumptions on the
properties of stellar populations. However, old metal-poor stars within the
Galaxy contain more $^{13}$C than is predicted, suggesting that further
refinements to the models are necessary. Gas at high redshift provides
important supplementary information at metallicities $-2\lesssim$ [Fe/H]
$\lesssim-1$, for which there are only a few measurements in the Galaxy. We
obtained new, high-quality, VLT/ESPRESSO observations of the QSO B1331+170 and
used them to measure $^{12}$C/$^{13}$C in the damped Lyman-$\alpha$ system
(DLA) at $z_{abs}=1.776$, with [Fe/H]=-1.27. AI-VPFIT, an Artificial
Intelligence tool based on genetic algorithms and guided by a spectroscopic
information criterion, was used to explore different possible kinematic
structures of the carbon gas. Three hundred independent AI-VPFIT models of the
absorption system were produced using pre-set $^{12}$C/$^{13}$C values, ranging
from 4 to 500. Our results show that $^{12}$C/$^{13}$C$=28.5^{+51.5}_{-10.4}$,
suggesting a possibility of $^{13}$C production at low metallicity.
