Molecular chaperones are known to be essential for avoiding protein aggregation in vivo, but it is still unclear how they affect protein folding mechanisms. We use single-molecule Förster resonance energy transfer to follow the folding of a protein inside the GroEL/GroES chaperonin cavity over a time range from milliseconds to hours. Our results show that confinement in the chaperonin decelerates the folding of the C-terminal domain in the substrate protein rhodanese, but leaves the folding rate of the N-terminal domain unaffected. Microfluidic mixing experiments indicate that strong interactions of the substrate with the cavity walls impede the folding process, but the folding hierarchy is preserved. Our results imply that no universal chaperonin mechanism exists. Rather, a competition between intra- and intermolecular interactions determines the folding rates and mechanisms of a substrate inside the GroEL/GroES cage.