  Using science verification observations obtained with ESPRESSO at the Very
Large Telescope (VLT) in 4UT mode, we report the first bound on the carbon
isotope ratio 12C/13C of a quiescent, near-pristine damped Ly-alpha (DLA)
system at z=2.34. We recover a limit log10(12C/13C) > +0.37 (2 sigma). We use
the abundance pattern of this DLA, combined with a stochastic chemical
enrichment model, to infer the properties of the enriching stars, finding the
total gas mass of this system to be log10(M_gas/M_sun)=6.3+1.4-0.9 and the
total stellar mass to be log10(M_*/M_sun)=4.8+/-1.3. The current observations
disfavour enrichment by metal-poor Asymptotic Giant Branch (AGB) stars with
masses <2.4 Msun, limiting the epoch at which this DLA formed most of its
enriching stars. Our modelling suggests that this DLA formed very few stars
until >1 Gyr after the cosmic reionization of hydrogen and, despite its very
low metallicity (~1/1000 of solar), this DLA appears to have formed most of its
stars in the past few hundred Myr. Combining the inferred star formation
history with evidence that some of the most metal-poor DLAs display an elevated
[C/O] ratio at redshift z<3, we suggest that very metal-poor DLAs may have been
affected by reionization quenching. Finally, given the simplicity and
quiescence of the absorption features associated with the DLA studied here, we
use these ESPRESSO data to place a bound on the possible variability of the
fine-structure constant, Delta alpha/alpha=(-1.2 +/- 1.1)x10^-5.
