  Chiral gauge groups acting on a lattice fermion field are constructed such
that all fermion modes (doublers) have the same charge. Details are given for
an abelian axial gauge group within a perturbative framework. An action based
on this group correctly reproduces the continuum gauge-current anomaly, while
preserving global chiral symmetry, locality, rotational symmetry and
hermiticity. A Wess-Zumino-like scalar field enters naturally to enforce exact
chiral gauge invariance. The degeneracy amongst the doublers can be lifted as
in a vector model.
