  We summarize our recent study of the fermion spectrum in a fermion-scalar 2D
model with a chiral $U(1)_L \times U(1)_R$ global symmetry. This model is
obtained from a two-cutoff lattice formulation of a 2D U(1) chiral gauge
theory, in the limit of zero gauge coupling. The massless fermion spectrum
found deep in the vortex phase is undoubled and chiral.
