  We investigate the possibility that neutrino capture on heavy nuclei competes
with beta decay in the environment where the $r$-Process elements are
synthesized. We find that such neutrino capture is not excluded by existing
abundance determinations. We show that inclusion of significant neutrino
capture on the (neutron number) N=82 waiting point nuclei can allow the
inferred abundances of these species to provide a good fit to steady weak (beta
decay plus neutrino capture) flow equilibrium. In fact, for particular choices
of neutrino flux conditions, this fit is improved over the case where nuclei
change their charge by beta decay alone. However, this improved fit can be
realized only if neutrino capture plays a negligible role in nuclear decay back
toward stability. We discuss the implications of these considerations for
current proposed sites and models for $r$-Process nucleosynthesis.
