We report measurements of the deuterium content of molecular hydrogen (H₂) obtained from a suite of air samples that were collected during a stratospheric balloon flight between 12 and 33 km at 40º N in October 2002. Strong deuterium enrichments of up to 400 permil versus Vienna Standard Mean Ocean Water (VSMOW) are observed, while the H₂ mixing ratio remains virtually constant. Thus, as hydrogen is processed through the H₂ reservoir in the stratosphere, deuterium is accumulated in H₂ . Using box model calculations we investigated the effects of H₂ sources and sinks on the stratospheric enrichments. Results show that considerable isotope enrichments in the production of H₂  from CH₄ must take place, i.e., deuterium is transferred preferentially to H₂ during the CH₄ oxidation sequence. This supports recent conclusions from tropospheric H₂ isotope measurements which show that H₂ produced photochemically from CH₄ and non-methane hydrocarbons must be enriched in deuterium to balance the tropospheric hydrogen isotope budget. In the absence of further data on isotope fractionations in the individual reaction steps of the CH₄ oxidation sequence, this effect cannot be investigated further at present. Our measurements imply that molecular hydrogen has to be taken into account when the hydrogen isotope budget in the stratosphere is investigated.