In order to operate in a coordinated fashion, multisubunit enzymes use cooperative interactions intrinsic to their enzymatic cycle, but this process remains poorly understood. Accordingly, ATP number distributions in various hydrolyzed states have been obtained for single copies of the mammalian double-ring multisubunit chaperonin TRiC/CCT in free solution using the emission from chaperonin-bound fluorescent nucleotides and closed-loop feedback trapping provided by an Anti-Brownian ELectrokinetic trap. Observations of the 16-subunit complexes as ADP molecules are dissociating shows a peak in the bound ADP number distribution at 8 ADP, whose height falls over time with little shift in the position of the peak, indicating a highly cooperative ADP release process which would be difficult to observe by ensemble-averaged methods. When AlFx is added to produce ATP hydrolysis transition state mimics (ADP·AlFx) locked to the complex, the peak at 8 nucleotides dominates for all but the lowest incubation concentrations. Although ensemble averages of the single-molecule data show agreement with standard cooperativity models, surprisingly, the observed number distributions depart from standard models, illustrating the value of these single-molecule observations in constraining the mechanism of cooperativity. While a complete alternative microscopic model cannot be defined at present, the addition of subunit-occupancy-dependent cooperativity in hydrolysis yields distributions consistent with the data.