The first stars, known as Population III (PopIII), produced the first heavy elements, thereby enriching their surrounding pristine gas. Previous detections of metals in intergalactic gas clouds, however, find a heavy element enrichment larger than $1/1000$ times that of the solar environment, higher than expected for PopIII remnants. In this letter we report the discovery of a Lyman limit system (LLS) at $z=3.53$ with the lowest metallicity seen in gas with discernable metals, $10^{-3.41pm0.26}$ times the solar value, at a level expected for PopIII remnants. We make the first relative abundance measurement in such low metallicity gas: the carbon-to-silicon ratio is $10^{-0.26pm0.17}$ times the solar value. This is consistent with models of gas enrichment by a PopIII star formation event early in the Universe, but also consistent with later, Population II enrichment. The metals in all three components comprising the LLS, which has a velocity width of 400 km s$^{-1}$, are offset in velocity by $sim+6$ km s$^{-1}$ from the bulk of the hydrogen, suggesting the LLS was enriched by a single event. Relative abundance measurements in this near-pristine regime open a new avenue for testing models of early gas enrichment and metal mixing.
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