Using calibrated FRET, we show that the simultaneous occupancy of both rings of GroEL by ATP and GroES occurs, leading to the rapid formation of symmetric GroEL:GroES2 "football" particles regardless of the presence or absence of substrate protein (SP). In the absence of SP, these symmetric particles revert to asymmetric GroEL:GroES1 "bullet" particles. The breakage of GroES symmetry requires the stochastic hydrolysis of ATP and the breakage of nucleotide symmetry. These asymmetric particles are both persistent and dynamic; they turnover via the asymmetric cycle. When challenged with SP, however, they revert to symmetric particles within a second. In the presence of SP, the symmetric particles are also persistent and dynamic. They turn over via the symmetric cycle. Under these conditions, the stochastic hydrolysis of ATP and the breakage of nucleotide symmetry also occur within the ensemble of particles. However, on account of SP-catalyzed ADP/ATP exchange, GroES symmetry is rapidly restored. The residence time of both GroES and SP on functional GroEL is reduced to ∼1 s, enabling many more iterations than was previously believed possible, consistent with the iterative annealing mechanism. This result is inconsistent with currently accepted models. Using a foldable SP, we show that as the SP folds to the native state and the population of unfolded SP declines, the population of symmetric particles reverts to asymmetric particles in parallel, a result that is consistent with the former being the folding functional form.