We solve a generalization of the chiral Schwinger model with a Wess-Zumino term in a covariant operator formalism. The model is essentially specified by two parameters (\ensuremath{\sigma},a), where \ensuremath{\sigma} measures the relative strength of the right- and left-handed gauge couplings (${e}_{R}$ and ${e}_{L}$) while a parametrizes the anomaly ambiguity. The fermion operator is constructed from the asymptotic boson fields in bosonized versions of the model. The model yields a sensible quantum theory in some restricted domain of \ensuremath{\sigma} and a. The gauge symmetry restored by the inclusion of the Wess-Zumino term gets spontaneously broken and the gauge field becomes massive. The fermion is confined as long as ${e}_{R}$${e}_{L}$\ensuremath{\ne}0. The model has a dual structure such that the model specified by (\ensuremath{\sigma},a) is equivalent to the model specified by another set (\ensuremath{\sigma}'=-\ensuremath{\sigma}, a'=a+2 sin2\ensuremath{\sigma}). This duality, in particular, reveals the equivalence of the Schwinger model and (a gauge-invariant version of) the axial Schwinger model.