  The first stars in the universe form inside $\sim 10^6 M_\odot$ dark matter
(DM) haloes whose initial density profiles are laid down by gravitational
collapse in hierarchical structure formation scenarios. During the formation of
the first stars in the universe, the baryonic infall compresses the dark matter
further. The resultant dark matter density is presented here, using an
algorithm originally developed by Young to calculate changes to the profile as
the result of adiabatic infall in a spherical halo model; the Young
prescription takes into account the non-circular motions of halo particles. The
density profiles obtained in this way are found to be within a factor of two of
those obtained using the simple adiabatic contraction prescription of
Blumenthal et al. Our results hold regardless of the nature of the dark matter
or its interactions and rely merely on gravity. If the dark matter consists of
weakly interacting massive particles, which are their own antiparticles, their
densities are high enough that their annihilation in the first protostars can
indeed provide an important heat source and prevent the collapse all the way to
fusion. In short, a ``Dark Star'' phase of stellar evolution, powered by DM
annihilation, may indeed describe the first stars in the universe.
