  We discuss the high energy neutrino emission from gamma-ray bursts resulting
from the earliest generation (`population III') stars forming in the Universe,
whose core collapses into a black hole. These gamma-ray bursts are expected to
produce a highly relativistic, magnetically dominated jet, where protons can be
accelerated to ultra-high energies. These interact with the photons produced by
the jet, leading to ultra-high energy photo-meson neutrinos as well as
secondary leptons and photons. The photon luminosity and the shock properties,
and thus the neutrino spectrum, depend on the mass of the black holes as well
as on the density of the surrounding external gas. We calculate the individual
source neutrino spectral fluxes and the expected diffuse neutrino flux for
various source parameters and evolution scenarios. Both the individual and
diffuse signals appear detectable in the 1-300 PeV range with current and
planned neutrino detectors such as IceCube and ARIANNA, provided the black hole
mass is in excess of 30-100 solar masses. This provides a possible test for the
debated mass of the progenitor stellar objects, as well as a probe for the
early cosmological environment and the formation rate of the earliest
structures.
