FeFe hydrogenases catalyze H2 oxidation and production using an "H-cluster", where two Fe ions are bound by an aza-dithiolate (adt) ligand. Various hypotheses have been proposed (by us and others) to explain that the enzyme reversibly inactivates under oxidizing, anaerobic conditions: intramolecular binding of the N atom of adt, formation of the so-called "Hox/inact" state or nonproductive binding of H2 to isomers of the H-cluster. Here, we show that none of the above explains the new finding that the anaerobic, oxidative, H2-dependent reversible inactivation is strictly dependent on the presence of Cl- or Br-. We provide experimental evidence that chloride uncompetitively inhibits the enzyme: it reversibly binds to catalytic intermediates of H2 oxidation (but not to the resting "Hox" state), after which oxidation locks the active site into a stable, saturated, inactive form, the structure of which is proposed here based on DFT calculations. The halides interact with the amine group of the H-cluster but do not directly bind to iron. It should be possible to stabilize the inhibited state in amounts compatible with spectroscopic investigations to explore further this unexpected reactivity of the H-cluster of hydrogenase.