  We study bulk fermion fields in the localized gravity model with
non-factorizable metric recently proposed by Randall and Sundrum, and
Gogberashvili. In addition to a tower of weak-scale Kaluza-Klein states we find
a zero mode for any value of the fundamental fermion mass. If the fermion mass
is larger than half the curvature of the compact dimension, the zero mode can
be localized on the ``hidden'' 3-brane in the Randall-Sundrum model.
Identifying this mode with a right-handed neutrino provides a new way for
obtaining small Dirac neutrino masses without invoking a see-saw mechanism.
Cancellation of the parity anomaly requires introducing an even number of bulk
fermions. This naturally leads to a strong hierarchy of neutrino masses and
generically large mixing angles.
