We present high-resolution observations of an extremely metal-poor damped Lyα system (DLA), at zabs= 2.340 0972 in the spectrum of the QSO J0035−0918, exhibiting an abundance pattern consistent with model predictions for the supernova yields of Population III stars. Specifically, this DLA has [Fe/H]≃−3, shows a clear ‘odd–even’ effect, and is C-rich with [C/Fe]=+1.53, a factor of ∼20 greater than reported in any other DLA. In analogy to the carbon-enhanced metal-poor stars in the Galactic halo (with [C/Fe] > +1.0), this is the first known case of a carbon-enhanced DLA. We determine an upper limit to the mass of 12C, M(12C) ≤ 200 M⊙, which depends on the unknown gas density n(H); if n(H) > 1 cm−3 (which is quite likely for this DLA given its low velocity dispersion), then M(12C) ≤ 2 M⊙, consistent with pollution by only a few prior supernovae. We speculate that DLAs such as the one discovered here may represent the ‘missing link’ between the yields of Population III stars and their later incorporation in the class of carbon-enhanced metal-poor stars which show no enhancement of neutron-capture elements (CEMP-no stars).