The GroEL/ES chaperonin system functions as a protein folding cage. Many obligate substrates of GroEL share the (βα)₈ TIM-barrel fold, but how the chaperonin promotes folding of these proteins is not known. Here, we analyzed the folding of DapA at peptide resolution using hydrogen/deuterium exchange and mass spectrometry. During spontaneous folding, all elements of the DapA TIM barrel acquire structure simultaneously in a process associated with a long search time. In contrast, GroEL/ES accelerates folding more than 30-fold by catalyzing segmental structure formation in the TIM barrel. Segmental structure formation is also observed during the fast spontaneous folding of a structural homolog of DapA from a bacterium that lacks GroEL/ES. Thus, chaperonin independence correlates with folding properties otherwise enforced by protein confinement in the GroEL/ES cage. We suggest that folding catalysis by GroEL/ES is required by a set of proteins to reach native state at a biologically relevant timescale, avoiding aggregation or degradation.