  We examine the dynamical evolution and statistical properties of the
supernova ejecta of massive primordial stars in a cosmological framework to
determine whether this first population of stars could have enriched the
universe to the levels and dispersions seen by the most recent observations of
the Lyman-Alpha forest. We evolve a lambda CDM model in a 1 Mpc^3 volume to a
redshift of z = 15 and add ``bubbles'' of metal corresponding to the supernova
ejecta of the first generation of massive stars in all dark matter halos with
masses greater than 5 times 10^5 solar masses. These initial conditions are
then evolved to z = 3 and the distribution and levels of metals are compared to
observations. In the absence of further star formation the primordial metal is
initially contained in halos and filaments. Photoevaporation of metal-enriched
gas due to the metagalactic ultraviolet background radiation at the epoch of
reionization (z ~ 6) causes a sharp increase of the metal volume filling
factor. At z = 3, ~ 2.5% of the simulation volume (approx. 20% of the total gas
mass) is filled with gas enriched above a metallicity of 10^-4 Z_solar, and
less than 0.6% of the volume is enriched above a metallicity of 10^-3 Z_solar.
This suggests that, even with the most optimistic prescription for placement of
primordial supernova and the amount of metals produced by each supernova, this
population of stars cannot entirely be responsible for the enrichment of the
Lyman-$\alpha$ forest to the levels and dispersions seen by current
observations unless we have severely underestimated the duration of the Pop III
epoch. However, comparison to observations show that Pop III supernovae can be
significant contributors to the very low overdensity Lyman-Alpha forest.
