We give a new description of classical Yang-Mills theory by coupling a two-dimensional chiral conformal field theory (which gives the tree-level S matrix of Yang-Mills theory at genus zero) to a background non-Abelian gauge field. The resulting model is solvable, and when the gravitational degrees of freedom are decoupled, the nonlinear Yang-Mills equations are imposed as an exact worldsheet anomaly cancellation condition. When gravitational modes are reinstated, we find gauge anomalies analogous to those appearing in heterotic string theory.