  Recent simulations of the formation of the first luminous objects in the
universe predict isolated very massive stars to form in dark matter halos with
virial temperatures large enough to allow significant amounts of molecular
hydrogen to form. We construct a semi-analytic model based on the
Press-Schechter formalism and calibrate the minimum halos mass that may form a
primordial star with the results from extensive adaptive mesh refinement
simulations. The model also includes star formation in objects with virial
temperatures in excess of ten thousand Kelvin. The free parameters are tuned to
match the optical depth measurements by the WMAP satellite. The models
explicitly includes the negative feedback of the destruction of molecular
hydrogen by a soft UV background which is computed self-consistently. We
predict high redshift supernova rates as one of the most promising tools to
test the current scenario of primordial star formation. The supernova rate from
primordial stars peaks at redshifts ~20. Using an analytic model for the
luminosities of pair-instability supernovae we predict observable magnitudes
and discuss possible observational strategies. Such supernovae would release
enough metals corresponding to a uniform enrichment to a few hundred thousands
of solar metalicity. If some of these stars produce gamma ray bursts our rates
will be directly applicable to understanding the anticipated results from the
SWIFT satellite. This study highlights the great potential for the James Webb
space telescope in probing cosmic structure at redshifts greater than 20.
