  We describe a proposal for constructing a lattice theory that we argue may be
capable of yielding free Weyl fermions in the continuum limit. The model
employs reduced staggered fermions and uses site parity dependent Yukawa
interactions of Fidkowski-Kitaev type to gap a subset of the lattice fermions
without breaking symmetries. The possibility for such symmetric mass generation
is tied to the cancellation of certain discrete anomalies arising in the
continuum limit. The latter place strong constraints on the number of lattice
fermions -- constraints that are satisfied by this model. We present numerical
results for the model in two dimensions which support this sc
