We present the first three-dimensional simulations to include the effects of dark matter annihilation feedback during the collapse of primordial minihalos. We begin our simulations from cosmological initial conditions and account for dark matter annihilation in our treatment of the chemical and thermal evolution of the gas. The dark matter is modeled using an analytical density profile that responds to changes in the peak gas density. We find that the gas can collapse to high densities despite the additional energy input from the dark matter. No objects supported purely by dark matter annihilation heating are formed in our simulations. However, we find that dark matter annihilation heating has a large effect on the evolution of the gas following the formation of the first protostar. Previous simulations without dark matter annihilation found that protostellar disks around Population III stars rapidly fragmented, forming multiple protostars that underwent mergers or ejections. When dark matter annihilation is included, however, these disks become stable to radii of 1000 AU or more. In the cases where fragmentation does occur, it is a wide binary that is formed.