  Recent theoretical investigations have suggested that the formation of the
very first stars, forming out of metal-free gas, was fundamentally different
from the present-day case. In this paper, we study the effect of metallicity on
the evolution of the gas in a collapsing dark matter mini-halo. We model such a
system as an isolated 3\sigma peak of mass 2x10^6 M_sun that collapses at
z_coll=30, using smoothed particle hydrodynamics. The gas has a supposed level
of pre-enrichment of either 10^-4 Z_sun or 10^-3 Z_sun. We find that the
evolution proceeds very differently for the two cases. The gas in the lower
metallicity simulation fails to undergo continued collapse and fragmentation,
whereas the gas in the higher metallicity case dissipatively settles into the
center of the dark matter halo. The central gas, characterized by densities n >
10^4 cm^-3, and a temperature, T \sim 90 K, which closely follows that of the
CMB, is gravitationally unstable and undergoes vigorous fragmentation. We
discuss the physical reason for the existence of a critical metallicity, Z_crit
\sim 5x10^-4 Z_sun, and its possible dependence on redshift. Compared to the
pure H/He case, the fragmentation of the 10^-3 Z_sun gas leads to a larger
relative number of low-mass clumps.
