  In order to constrain the initial mass function (IMF) of the first generation
of stars (Population III), we investigate the fragmentation properties of
metal-free gas in the context of a hierarchical model of structure formation.
We investigate the evolution of an isolated 3-sigma peak of mass 2x10^6 M_solar
which collapses at z_coll=30 using Smoothed Particle Hydrodynamics. We find
that the gas dissipatively settles into a rotationally supported disk which has
a very filamentary morphology. The gas in these filaments is Jeans unstable
with M_J~10^3 M_solar. Fragmentation leads to the formation of high density
(n>10^8 cm^-3) clumps which subsequently grow in mass by accreting surrounding
gas and by merging with other clumps up to masses of ~10^4 M_solar. This
suggests that the very first stars were rather massive. We explore the complex
dynamics of the merging and tidal disruption of these clumps by following their
evolution over a few dynamical times.
