The structure and evolution of a protostar forming from a cloud composed of pure hydrogen and helium gas are calculated. Using an accretion rate of 0.0044 solar mass/yr, the collapse of the cloud is followed numerically as a sequence of steady state accretion flows onto the hydrostatic core, which grows from an initial mass of 0.01 solar mass to 10.5 solar masses. The core is surrounded by an optically thick radiative precursor for most of its evolution. The core radius reaches 47 solar radii when the mass is 1 solar mass. For sufficiently massive cores, the deep interior contracts strongly, driving out a 'luminosity wave' which reaches the surface when the mass is 8 solar masses. This results in a large increase in core radius, the establishment of surface convection, and the disappearance of the radiative precursor. The dependence of core radius on the mass and accretion rate is analytically derived, and a new table or Rosseland mean opacities for metal-free gas is presented.