  We model gas cooling in high-resolution N-body simulations in order to
investigate the formation of the first generation of stars. We follow a region
of a LCDM universe especially selected to contain a rich cluster by the present
day. The properties of the dark haloes that form in these sub-solar mass
resolution simulations are presented in a companion paper by Gao et al. The
first gas clouds able to cool by molecular hydrogen line emission collapse at
extremely high redshift, z ~ 47, when the mass of the dark halo is 2.4 x 10^5
Msun/h. By z ~ 30, a substantial population of haloes are capable of undergoing
molecular hydrogen cooling although their ability to form stars is dependent on
the efficiency of feedback processes such as dissociating Lyman-Werner
radiation. The mass of the main halo grows extremely rapidly and, by z ~ 36,
its virial temperature has reached 10^4K, at which point gas cooling becomes
dominated by more effective atomic line processes. By z ~ 30, a small ``group''
of such potential galaxies will have formed unless prevented from doing so by
feedback processes. By this redshift, massive (>~ 100 Msun) population III
stars are able to ionise gas well beyond their own host halo and neighbouring
HII regions can percolate to form an ionized superbubble. Such patches would be
too widely separated to contribute significantly to reionisation at this time.
The large number density of early cooling haloes in the pre-reionised universe
raises the exciting prospect that this ultra-early generation of stars may be
observable as gamma-ray bursts or supernovae.
