Chaperonins use energy derived from ATP hydrolysis to enhance the efficiency of protein folding by a mechanism which remains a matter of debate. Here, we show that the kinetics of spontaneous and assisted folding of mitochondrial malate dehydrogenase are quantitatively described by a simple physical model. The protein folds from non-native chains by the slow formation of native-like monomers, which then dimerize to form the active enzyme. Misfolding proceeds by two phases of aggregation: the first is slowly reversible, the second is irreversible. Chaperonins accelerate the dissociation of the first-formed, unstable aggregates through a repeated binding-and-release cycle coupled to ATP hydrolysis. By this catalytic action, they supply the productive folding pathway with monomers, and block the irreversible phase of aggregation, thereby maintaining optimal folding yields even when present in sub-stoichiometric quantities. The hydrolytically active chaperonin is required until the substrate protein has completed the slow transition to its native-like, monomeric state. Both the observed rate of folding and the yield are increased by this mechanism without changing real rates in the productive pathway.