The transformation of atomic hydrogen to molecular hydrogen through three-body reactions is a crucial stage in the collapse of primordial, metal-free halos, where the first generation of stars (Population III stars) in the universe is formed. However, in the published literature, the rate coefficient for this reaction is uncertain by nearly an order of magnitude. We report on the results of both adaptive mesh refinement and smoothed particle hydrodynamics simulations of the collapse of metal-free halos as a function of the value of this rate coefficient. For each simulation method, we have simulated a single halo three times, using three different values of the rate coefficient. We find that while variation between halo realizations may be greater than that caused by the three-body rate coefficient being used, both the accretion physics onto Population III protostars as well as the long-term stability of the disk and any potential fragmentation may depend strongly on this rate coefficient.