We describe a theory living on the null conformal boundary I of four-dimensional Minkowski space, the states of which include the radiative modes of Yang–Mills theory. The action of a Kac–Moody symmetry algebra on the correlators of these states leads to a Ward identity for asymptotic “large” gauge transformations which is equivalent to the soft gluon theorem. The subleading soft gluon behavior is also obtained from a Ward identity for charges acting as vector fields on the sphere of null generators of I. Correlation functions of the Yang–Mills states are shown to produce the full classical S-matrix of Yang–Mills theory. The model contains additional states arising from nonunitary gravitational degrees of freedom, indicating a relationship with the twistor string of Berkovits and Witten.