  We consider nucleosynthesis constraints on models which use chiral symmetry
breaking as a basis for understanding very small Dirac neutrino masses. We show
that present big-bang nucleosynthesis constraints impose a well-defined upper
bound of 0.1eV on the neutrino masses. This bound may become several orders of
magnitude more stringent in the future as our understanding of the
observational constraints on nucleosynthesis improves. We discuss the
phenomenological implications for neutrino dark matter, the solar neutrino
problem and the atmospheric neutrino deficit.
