  We consider the relic neutrino background produced by Population III stars
coupled with a normal mode of star formation at lower redshift. The computation
is performed in the framework of hierarchical structure formation and is based
on cosmic star formation histories constrained to reproduce the observed star
formation rate at redshift z \la 6, the observed chemical abundances in damped
Lyman alpha absorbers and in the intergalactic medium, and to allow for an
early reionization of the Universe at z ~ 10-20. We consider both a burst and
non-burst model for Population III star formation. We find that although the
high redshift burst of Population III stars does lead to an appreciable flux of
neutrinos at relatively low energy (E_\nu \approx 1 MeV), the observable
neutrino flux is dominated by the normal mode of star formation. We also find
that predicted fluxes are at the present level of the SuperK limit. As a
consequence, the supernova relic neutrino background has a direct impact on
models of chemical evolution and/or supernova dynamics.
