Facilitated protein folding by the double toroidal bacterial chaperonin, GroEL/GroES, proceeds by a "two-stroke engine" mechanism in which an allosteric interaction between the two rings synchronizes the reaction cycle by controlling the binding and release of cochaperonin. Using chimeric chaperonin molecules assembled by fusing equatorial and apical domains derived from GroEL and its mammalian mitochondrial homolog, Hsp60, we show that productive folding by Hsp60 and its cognate cochaperonin, Hsp10, proceeds in vitro and in vivo without the formation of a two-ring structure. This simpler "one-stroke" engine works because Hsp60 has a different mechanism for the release of its cochaperonin cap and bound target protein.