  We present an alternative derivation of the parity anomaly for a massless
Dirac field in 2+1 dimensions coupled to a gauge field. The anomaly functional,
a Chern-Simons action for the gauge field, is obtained from the non-trivial
Jacobian corresponding to a non local symmetry of the Pauli-Villars regularized
action. That Jacobian is well-defined, finite, and yields the standard
Chern-Simons term when the cutoff tends to infinity.
