  We show that the 3450 U(1) chiral fermion theory can appear as the low energy
effective field theory of a 1+1D local lattice model, with an on-site U(1)
symmetry and finite-range interactions. The on-site U(1) symmetry means that
the U(1) symmetry can be gauged (gaugeable for both background probe and
dynamical fields), which leads to a non-perturbative definition of chiral gauge
theory --- a chiral fermion theory coupled to U(1) gauge theory. Our
construction can be generalized to regularize any U(1)-anomaly-free 1+1D gauged
chiral fermion theory with a zero chiral central charge (thus no gravitational
anomaly) by a lattice, thanks to the recently proven "Poincar\'e dual"
equivalence between the U(1) 't Hooft anomaly free condition and the U(1)
symmetric interaction gapping rule, via a bosonization-fermionization
technique.
