  We show that the recently observed elemental abundance pattern of the
carbon-rich metal-poor Damped Lyman $\alpha$ (DLA) system is in excellent
agreement with the nucleosynthesis yields of faint core-collapse supernovae of
primordial stars. The observed abundance pattern is not consistent with the
nucleosynthesis yields of pair-instability supernovae. The DLA abundance
pattern is very similar to that of carbon-rich extremely metal-poor (EMP)
stars, and the contributions from low-mass stars and/or binary effects should
be very small in DLAs. This suggests that chemical enrichment by the first
stars in the first galaxies is driven by core-collapse supernovae from $\sim
20-50 M_\odot$ stars, and also supports the supernova scenario as the
enrichment source of EMP stars in the Milky Way Galaxy.
