In their paper Gauge Theory and Integrability III, Costello and Yamazaki use four-dimensional Chern-Simons theory to predict the existence of a novel class of integrable two-dimensional sigma models. In particular, they predict the existence of certain geometric structures on an open subspace of the moduli of G-bundles on an algebraic curve. In this talk I will construct these structures and show that the resulting sigma model has a zero-curvature formulation. I further promise to present a concrete example.