ATP-dependent allosteric regulation of the ring-shaped group II chaperonins remains ill defined, in part because their complex oligomeric topology has limited the success of structural techniques in suggesting allosteric determinants. Further, their high sequence conservation has hindered the prediction of allosteric networks using mathematical covariation approaches. Here, we develop an information theoretic strategy that is robust to residue conservation and apply it to group II chaperonins. We identify a contiguous network of covarying residues that connects all nucleotide-binding pockets within each chaperonin ring. An interfacial residue between the networks of neighboring subunits controls positive cooperativity by communicating nucleotide occupancy within each ring. Strikingly, chaperonin allostery is tunable through single mutations at this position. Naturally occurring variants at this position that double the extent of positive cooperativity are less prevalent in nature. We propose that being less cooperative than attainable allows chaperonins to support robust folding over a wider range of metabolic conditions.