In order to characterize damped Lyα absorption systems (DLAs) potentially hosting first stars, we present a novel approach to investigate DLAs in the context of Milky Way (MW) formation, along with their connection with the most metal-poor stars and local dwarf galaxies. The merger tree method previously developed is extended to include inhomogeneous reionization and metal mixing, and it is validated by matching both the metallicity distribution function of Galactic halo stars and the Fe–luminosity relation of dwarf spheroidal galaxies. The model explains the observed –Fe relation of DLAs along with the chemical abundances of [Fe/H] < −2 systems. In this picture, the recently discovered zabs≈ 2.34 C-enhanced DLA pertains to a new class of absorbers hosting first stars along with second-generation long-living low-mass stars. These ‘Population III DLAs’ are the descendants of H2-cooling minihaloes with , which virialize at z > 8 in neutral, primordial regions of the MW environment and passively evolve after a short initial period of star formation. The gas in these systems is warm K, and strongly C-enriched by long-living, extremely metal-poor stars of total mass M*≈ 102–104 M⊙.