We reconsider the model of neutrino production during the bright phase, first suggested in 1977, in the light of modern understanding of the role of Pop III stars and acceleration of particles in supernova shocks. We concentrate on the production of cosmogenic UHE neutrinos in supernova explosions that accompany the death of Pop III stars. Accelerated protons produce neutrinos in collisions with CMB photons. We deliberately use simplified assumptions which make our results transparent. Pop III stars are assumed to be responsible for the reionization of the universe as observed by WMAP. Since the evolution of Pop III stars is much faster than the Hubble rate, we consider the burst of UHE proton production to occur at fixed redshift (z_b=10-20). We discuss the formation of collisionless shocks and particle acceleration in the early universe. The composition of accelerated particles is expected to be proton dominated. A simple calculation is presented to illustrate the fact that the diffuse neutrinos flux from the bright phase burst is concentrated in a relatively narrow range around $7.5 times 10^{15}(20/z_b)^2$ eV. The $ u_mu$ flux may be detectable by IceCube without violating the cascade upper limit and the expected energetics of SNe associated with Pop III stars. A possible signature of the neutrino production from Pop III stars may be the detection of resonant neutrino events. For the burst at $z_b=20$ and $bar{ u}_e$-flux at the cascade upper limit, the number of resonant events in IceCube may be as high as 10 events in 5 years of observations. These events have equal energies, $E=6.3times 10^{15}$ eV, in the form of e-m cascades. Given the large uncertainties in the existing predictions of UHE cosmogenic neutrino fluxes, we argue that neutrinos from the first stars might become one of the most reliable hopes for UHE neutrino astronomy.
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