A multi-stage, isothermal, carbon monoxide preferential oxidation (PrOx) reactor comprising a plurality of serially arranged, catalyzed heat exchangers, each separated from the next by a mixing chamber for homogenizing the gases exiting one heat exchanger and entering the next. In a preferred embodiment, at least some of the air used in the PrOx reaction is injected directly into the mixing chamber between the catalyzed heat exchangers.