We have studied (l+l)-dimensional gauge theory with the chiral fermions using the path-integral approach. Performing a non-abelian chiral change of variables and choosing a more general regularization operator, we get the exact solution of the fermion determinant. We also show that there can exist a mass generation in the theory for the vector bosons. Apart from a mass term, the solution contains a gauged Wess-Zumino-Witten anomaly functional and some other non-local terms.