  We study the formation of the first generation of stars in the standard cold
dark matter model, using a very high-resolution hydordynamic simulations. Our
simulation achieves a dynamic range of 10^{10} in length scale. With accurate
treatment of atomic and molecular physics, it allows us to study the
chemo-thermal evolution of primordial gas clouds to densities up to n =
10^{16}/cc without assuming any a priori equation of state; a six orders of
magnitudes improvement over previous three-dimensional calculations. All the
relevant atomic and molecular cooling and heating processes, including cooling
by collision-induced continuum emission, are implemented. For calculating
optically thick H2 cooling at high densities, we use the Sobolev method. To
examine possible gas fragmentation owing to thermal instability, we compute
explicitly the growth rate of isobaric perturbations. We show that the cloud
core does not fragment in either the low-density or high-density regimes. We
also show that the core remains stable against gravitational deformation and
fragmentation. We obtain an accurate gas mass accretion rate within a 10 Msun
innermost region around the protostar. The protostar is accreting the
surrounding hot gas at a rate of 0.001-0.01 Msun/yr. From these findings we
conclude that primordial stars formed in early minihalos are massive. We carry
out proto-stellar evolution calculations using the obtained accretion rate. The
resulting mass of the first star is M_ZAMS = 60-100 Msun, with the exact mass
dependent on the actual accretion rate.
