We present a method for measuring the clumped isotope composition of molecular hydrogen (H2) using a high-resolution mass spectrometer, the Thermo 253 Ultra, improved to address subtle artifacts arising from instrument baselines and non-linear responses. We also present methods for purification and concentration of H2 from natural and experimental samples, tailored to this measurement. We document the accuracy of the method through comparison to established methods for the determination of δD values, and through measurements of H2 gases of widely varying D content that were driven to isotopic equilibrium with respect to their distributions of isotopologues by heating in the presence of a catalyst. Experimental reproducibility of δD and ΔDD values over months averages ±0.5 and ± 6.9 ‰, respectively (1σ) — both small fractions of common natural variations. We explore methods of gas purification and handling, and show that preferred methods result in low (0–4 ‰) changes in δD and undetectable changes in ΔDD. Our methods and data processing procedures were further tested by comparing measurements of mixtures of H2 gases that varied widely in δD and ∆DD with a model describing proportions of isotopologues in such mixtures. Application of these methods to H2 that is residual to laboratory consumption by cultured methanogens shows that metabolic ‘back reaction’ (metabolic production of H2 from water-derived protons during net H2 consumption) is responsible for driving the ΔDD value of residual H2 toward equilibrium at environmental temperatures. Finally, we report the first measurements of the clumped isotope composition of molecular hydrogen in natural geological samples collected from high and low temperature submarine hydrothermal vents (Lost city, Rainbow, Ashadze) and an intracontinental natural reservoir in Mali; initial findings suggest that ∆DD of H2 generally records temperatures of fluid venting or long-term storage, even in cases where the δD of H2 has not equilibrated with water at those temperatures. This study establishes the first clumped isotope systematics of molecular hydrogen based on both experimental and natural samples, including key processes in the biogeochemical cycle of H2.