  Recent simulations of Population III star formation have suggested that some
fraction form in binary systems, in addition to having a characteristic mass of
tens of solar masses. The deaths of metal-free stars result in the initial
chemical enrichment of the universe and the production of the first
stellar-mass black holes. Here we present a cosmological adaptive mesh
refinement simulation of an overdense region that forms a few 10^9 Msun dark
matter halos and over 13,000 Population III stars by redshift 15. We find that
most halos do not form Population III stars until they reach Mvir ~ 10^7 Msun
because this biased region is quickly enriched from both Population III and
galaxies, which also produce high levels of ultraviolet radiation that suppress
H2 formation. Nevertheless, Population III stars continue to form, albeit in
more massive halos, at a rate of ~ 10^{-4} Msun yr^{-1} Mpc^{-3} at redshift
15. The most massive starless halo has a mass of 7 x 10^7 Msun, which could
host massive black hole formation through the direct gaseous collapse scenario.
We show that the multiplicity of the Population III remnants grows with halo
mass above 10^8 Msun, culminating in 50 remnants located in 10^9 Msun halos on
average. This has implications that high mass X-ray binaries and intermediate
mass black holes that originate from metal-free stars may be abundant in
high-redshift galaxies.
