All lattice formulations of gauge theories containing fermions in chiral representations of the gauge group reduce in the weak-coupling limit to theories of fermions and scalars with a residual global chiral symmetry. A generic type of these models are the so-called Wilson-Yukawa models that were extensively studied some years ago, and their fermionic spectrum was always found to be vectorlike. The weak-coupling limit of a recent formulation of lattice fermions is shown to give rise to a modified version of Wilson-Yukawa models with a different phase structure. In particular a new phase is found containing massless fermions with chiral quantum numbers. This is the correct phase to find neutrinos on the lattice.