Chains of interacting anyons, such as the “Golden chain”, exhibit rich phase diagrams, with both extended critical regions, as well as gapped phases. In this talk, the integrability of a particular anyonic chain, with competing two- and three-body interactions will be examined. We will construct an R-matrix which satisfies the Yang-Baxter equation for a finite range of interactions. To obtain information about the behaviour of the chain, we will employ the Corner Transfer Matrix method, and find the critical behaviour for a particular interaction.

IHP