We construct lattice theories from reduced staggered fermions that we argue are capable of producing
chiral theories in the continuum limit. The construction employs Yukawa interactions of Fidkowski-Kitaev type to generate cut-off scale masses for half of the lattice fermions while preserving all symmetries. We argue that the remaining lattice fermions organize themselves in the continuum limit into a set of Majorana fermions. In four dimensions the Majorana fermions are massless and equivalent to sixteen Weyl fermions
as required for the cancellation of certain discrete anomalies.