TRiC is an important group II chaperonin that facilitates the folding of many eukaryotic proteins. The TRiC complex consists of two stacked rings, each comprised of eight paralogous subunits with a mutual sequence identity of 30-35%. Each subunit has unique functional roles that are manifested by corresponding sequence conservation. It is generally assumed that the subunit order within each ring is fixed, but this order is still uncertain. Here we address the problem of the intra-ring subunit order by combining two sources of information: evolutionary conservation and a structural hypothesis. Specifically, we identify residues in the TRiC subunits that are likely to be part of the intra-unit interface, based on homology modeling to the solved thermosome structure. Within this set of residues, we search for a subset that shows an evolutionary conservation pattern that is indicative of the subunit order key. This pattern shows considerable conservation across species, but large variation across the eight subunits. By this approach we were able to locate two parts of the interface where complementary interactions seem to favor certain pairing of subunits. This knowledge leads to restrictions on the 5,040 (=7!) possible subunits arrangements in the ring, and limits them to just 72. Although our findings give only partial understanding of the inter-subunit interactions that determine their order, we conclude that they are comprised of complementary charged, polar and hydrophobic interactions that occur in both the equatorial and middle domains of each subunit.