A Classical Version of the Non-Abelian Gauge Anomaly

We show that a version of the covariant gauge anomaly for a 3+1 dimensional chiral fermion interacting with a non-Abelian gauge field can be obtained from the classical Hamiltonian flow of its probability distribution in phase space. The only quantum input needed is the Berry phase that arises from the direction of the spin being slaved to the particle's momentum.