  We simulate the growth of a Population III stellar system, starting from
cosmological initial conditions at z=100. We follow the formation of a minihalo
and the subsequent collapse of its central gas to high densities, resolving
scales as small as ~ 1 AU. Using sink particles to represent the growing
protostars, we model the growth of the photodissociating and ionizing region
around the first sink, continuing the simulation for ~ 5000 yr after initial
protostar formation. Along with the first-forming sink, several tens of
secondary sinks form before an ionization front develops around the most
massive star. The resulting cluster has high rates of sink formation, ejections
from the stellar disc, and sink mergers during the first ~ 2000 yr, before the
onset of radiative feedback. By this time a warm ~ 5000 K phase of neutral gas
has expanded to roughly the disc radius of 2000 AU, slowing mass flow onto the
disc and sinks. By 5000 yr the most massive star grows to 20 M_sol, while the
total stellar mass approaches 75 M_sol. Out of the ~ 40 sinks, approximately 30
are low-mass (M_* < 1 M_sol), and if the simulation had resolved smaller scales
an even greater number of sinks might have formed. Thus, protostellar radiative
feedback is insufficient to prevent rapid disc fragmentation and the formation
of a high-member Pop III cluster before an ionization front emerges. Throughout
the simulation, the majority of stellar mass is contained within the most
massive stars, further implying that the Pop III initial mass function is
top-heavy.
