All real processes, be they chemical, mechanical or electrical, are thermodynamically irreversible and therefore suffer from thermodynamic losses. Here, we report the design and operation of a chemical reactor capable of approaching thermodynamically reversible operation. The reactor was employed for hydrogen production via the water–gas shift reaction, an important route to ‘green’ hydrogen. The reactor avoids mixing reactant gases by transferring oxygen from the (oxidizing) water stream to the (reducing) carbon monoxide stream via a solid-state oxygen reservoir consisting of a perovskite phase (La 0.6 Sr 0.4 FeO 3-δ ). This reservoir is able to remain close to equilibrium with the reacting gas streams because of its variable degree of non-stoichiometry and thus develops a ‘chemical memory’ that we employ to approach reversibility. We demonstrate this memory using operando, spatially resolved, real-time, high-resolution X-ray powder diffraction on a working reactor. The design leads to a reactor unconstrained by overall chemical equilibrium limitations, which can produce essentially pure hydrogen and carbon dioxide as separate product streams.