  We consider theories with gauged chiral fermions in which there are abelian
anomalies, and no nonabelian anomalies (but there may be nonabelian gauge
fields present). We construct an associated theory that is gauge invariant,
renormalizable, and with the same particle content, by adding a finite number
of terms to the action. Alternatively one can view the new theory as arising
from the original theory by using another regularization, one that is gauge
invariant. The situation is reminiscent of the mechanism of adding Fadeev-Popov
ghosts to an unsatisfactory gauge theory, to arrive at the usual quantization
procedure. The models developed herein are much like the abelian Wess-Zumino
model (an abelian effective theory with a Wess-Zumino counter term), but unlike
the W-Z model are renormalizable!
