We have performed the first ever combined-element stable isotopic measurements of extraterrestrial molecules. Methane from two carbonaceous chondrites, Murchison and Cold Bokkeveld, was measured for its hydrogen and carbon isotopic compositions. The combined isotopic composition of meteoritic methane reveals information about the indigenous nature of volatile aliphatic organic matter in meteorites and its probable extraterrestrial source environment. Deuterium enrichments relative to the solar nebula 4.6 Gyr ago reflect a contribution from low-temperature chemical reactions in interstellar space. Similar carbon but different hydrogen isotopic compositions for methane in the two meteorite samples probably represent comparable primary origins but varying levels of secondary processing and exchange with isotopically light hydrogen. Our high precision laboratory-obtained measurements provide valuable reference points for observational spectroscopists undertaking astronomical investigations of the stable isotopic composition of extraterrestrial methane.