jats:titleAbstract</jats:title> jats:pWe present precise abundance determinations of two near-pristine damped Lyjats:italicα</jats:italic> systems (DLAs) to assess the nature of the [O/Fe] ratio at [Fe/H] < −3.0 (i.e., <1/1000 of the solar metallicity). Prior observations indicate that the [O/Fe] ratio is consistent with a constant value, [O/Fe] ≃ +0.4, when −3 < [Fe/H] < −2, but this ratio may increase when [Fe/H] ≲ −3. In this paper, we test this picture by reporting new, high-precision [O/Fe] abundances in two of the most metal-poor DLAs currently known. We derive values of [O/Fe] = +0.50 ± 0.10 and [O/Fe] = +0.62 ± 0.05 for these two jats:italicz</jats:italic> ≃ 3 near-pristine gas clouds. These results strengthen the idea that the [O/Fe] abundances of the most metal-poor DLAs are elevated compared to DLAs with [Fe/H] ≳ −3. We compare the observed abundance pattern of the latter system to the nucleosynthetic yields of Population III supernovae (SNe), and find that the enrichment can be described by a (19–25) Mjats:sub⊙</jats:sub> Population III SN that underwent a (0.9–2.4) × 10jats:sup51</jats:sup> erg explosion. These high-precision measurements showcase the behavior of [O/Fe] in the most metal-poor environments. Future high-precision measurements in new systems will contribute to a firm detection of the relationship between [O/Fe] and [Fe/H]. These data will reveal whether we are witnessing a chemical signature of enrichment from Population III stars and allow us to rule out contamination from Population II stars.</jats:p>