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 . The question then arises which effect was responsible for this transition in the star formation properties . 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 2 \times 10 ^ { 6 } M _ { \odot } that collapses at z _ { coll } \simeq 30 , using smoothed particle hydrodynamics . The gas has a supposed level of pre-enrichment of either Z = 10 ^ { -4 } Z _ { \odot } or 10 ^ { -3 } Z _ { \odot } . We assume that H _ { 2 } has been radiatively destroyed by the presence of a soft UV background . Metals therefore provide the only viable cooling at temperatures below 10 ^ { 4 } K. 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 centre of the dark matter halo . The central gas , characterized by densities n _ { \mathrm { H } } \ga 10 ^ { 4 } cm ^ { -3 } , and a temperature , T \simeq 90 K , which closely follows that of the cosmic microwave background , is gravitationally unstable and undergoes vigorous fragmentation . We discuss the physical reason for the existence of a critical metallicity , Z _ { crit } \sim 5 \times 10 ^ { -4 } Z _ { \odot } , and its possible dependence on redshift . Compared to the pure H/He case , the fragmentation of the Z = 10 ^ { -3 } Z _ { \odot } gas leads to a larger relative number of low-mass clumps .