In response to warming climate, methane can be released to Arctic Ocean sediment and waters from thawing subsea permafrost and decomposing methane hydrates. However, it is unknown whether methane derived from this sediment storehouse of frozen ancient carbon reaches the atmosphere. We quantified the fraction of methane derived from ancient sources in shelf waters of the U.S. Beaufort Sea, a region that has both permafrost and methane hydrates and is experiencing significant warming. Although the radiocarbon-methane analyses indicate that ancient carbon is being mobilized and emitted as methane into shelf bottom waters, surprisingly, we find that methane in surface waters is principally derived from modern-aged carbon. We report that at and beyond approximately the 30-m isobath, ancient sources that dominate in deep waters contribute, at most, 10 ± 3% of the surface water methane. These results suggest that even if there is a heightened liberation of ancient carbon–sourced methane as climate change proceeds, oceanic oxidation and dispersion processes can strongly limit its emission to the atmosphere.