Saturn's moon Enceladus has an ice-covered ocean; a plume of material erupts from cracks in the ice. The plume contains chemical signatures of water-rock interaction between the ocean and a rocky core. We used the Ion Neutral Mass Spectrometer onboard the Cassini spacecraft to detect molecular hydrogen in the plume. By using the instrument's open-source mode, background processes of hydrogen production in the instrument were minimized and quantified, enabling the identification of a statistically significant signal of hydrogen native to Enceladus. We find that the most plausible source of this hydrogen is ongoing hydrothermal reactions of rock containing reduced minerals and organic materials. The relatively high hydrogen abundance in the plume signals thermodynamic disequilibrium that favors the formation of methane from CO2 in Enceladus' ocean.