We examine aspects of primordial star formation in the presence of a molecular hydrogen-dissociating ultraviolet background . We compare a set of AMR hydrodynamic cosmological simulations using a single cosmological realization but with a range of ultraviolet background strengths in the Lyman-Werner band . This allows us to study the effects of Lyman-Werner radiation on suppressing H _ { 2 } cooling at low densities as well as the high-density evolution of the collapsing cloud core in a self-consistent cosmological framework . We find that the addition of a photodissociating background results in a delay of the collapse of high density gas at the center of the most massive halo in the simulation and , as a result , an increase in the virial mass of this halo at the onset of baryon collapse . We find that , contrary to previous results , Population III star formation is not suppressed for J _ { 21 } \geq 0.1 , but occurs even with backgrounds as high as J _ { 21 } = 1 . We find that H _ { 2 } cooling leads to collapse despite the depressed core molecular hydrogen fractions due to the elevated H _ { 2 } cooling rates at T = 2 - 5 \times 10 ^ { 3 } K. We observe a relationship between the strength of the photodissociating background and the rate of accretion onto the evolving protostellar cloud core , with higher LW background fluxes resulting in higher accretion rates . Finally , we find that the collapsing cloud cores in our simulations do not fragment at densities below n \sim 10 ^ { 10 } cm ^ { -3 } regardless of the strength of the LW background , suggesting that Population III stars forming in halos with T _ { vir } \sim 10 ^ { 4 } K may still form in isolation .