We summarize our recent study [1] of the fermion spectrum in a fermion-scalar 2D model with a chiral U(1)(L) x U(1)(R) global symmetry. This model is obtained from a two-cutoff 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.