During and after protein translation, molecular chaperones require ATP hydrolysis to favor the native folding of their substrates and, under stress, to avoid aggregation and revert misfolding. Why do some chaperones need ATP, and what are the consequences of the energy contributed by the ATPase cycle? Here, we used biochemical assays and physical modeling to show that the bacterial chaperones GroEL (Hsp60) and DnaK (Hsp70) both use part of the energy from ATP hydrolysis to restore the native state of their substrates, even under denaturing conditions in which the native state is thermodynamically unstable. Consistently with thermodynamics, upon exhaustion of ATP, the metastable native chaperone products spontaneously revert to their equilibrium non-native states. In the presence of ATPase chaperones, some proteins may thus behave as open ATP-driven, nonequilibrium systems whose fate is only partially determined by equilibrium thermodynamics.