  We perform numerical simulations of the growth of a Population III stellar
system under photodissociating feedback. We start from cosmological initial
conditions at z = 100, self-consistently following the formation of a minihalo
at z = 15 and the subsequent collapse of its central gas to high densities. The
simulations resolve scales as small as ~ 1 AU, corresponding to gas densities
of 10^16 cm^-3. Using sink particles to represent the growing protostars, we
evolve the stellar system for the next 5000 years. We find that this emerging
stellar group accretes at an unusually low rate compared with minihalos which
form at earlier times (z = 20 - 30), or with lower baryonic angular momentum.
The stars in this unusual system will likely reach masses ranging from < 1
M_sun to 5 M_sun by the end of their main-sequence lifetimes, placing them in
the mass range for which stars will undergo an asymptotic giant branch (AGB)
phase. Based upon the simulation, we predict the rare existence of Population
III stars that have survived to the present day and have been enriched by mass
overflow from a previous AGB companion.
