  We report results from a cosmological simulation with non-equilibrium
chemistry of 21 species, including H2, HD, and LiH molecular cooling. Starting
from cosmological initial conditions, we focus on the evolution of the central
1.8 Kpc region of a 3 x 10^7 Msun halo. The crossing of a few 10^6 Msun halos
and the gas accretion through larger scale filaments generate a turbulent
environment within this region. Due to the short cooling time caused by the
non-equilibrium formation of H2, the supersonic turbulence results in a very
fragmented mass distribution, where dense, gravitationally unstable clumps
emerge from a complex network of dense filaments. At z=10.87, we find
approximately 25 well defined, gravitationally unstable clumps, with masses of
4 x 10^3-9 x 10^5 Msun, temperatures of approximately 300K, and cooling times
much shorter than the free-fall time. Only the initial phase of the collapse of
individual clumps is spatially resolved in the simulation. Depending on the
density reached in the collapse, the estimated average Bonnor-Ebert masses are
in the range 200-800 Msun. We speculate that each clump may further fragment
into a cluster of stars with a characteristic mass in the neighborhood of 50
Msun. This process at z ~ 11 may represent the dominant mode of Pop. III star
formation, causing a rapid chemical enrichment of the protogalactic
environment.
