Molecular hydrogen (H2) is the second most abundant trace gas in the atmosphere after methane (CH4). In the troposphere, the D/H ratio of H2 is enriched by 120 per thousand relative to the world's oceans. This cannot be explained by the sources of H2 for which the D/H ratio has been measured to date (for example, fossil fuels and biomass burning). But the isotopic composition of H2 from its single largest source--the photochemical oxidation of methane--has yet to be determined. Here we show that the D/H ratio of stratospheric H2 develops enrichments greater than 440 per thousand, the most extreme D/H enrichment observed in a terrestrial material. We estimate the D/H ratio of H2 produced from CH4 in the stratosphere, where production is isolated from the influences of non-photochemical sources and sinks, showing that the chain of reactions producing H2 from CH4 concentrates D in the product H2. This enrichment, which we estimate is similar on a global average in the troposphere, contributes substantially to the D/H ratio of tropospheric H2.