We present a particle physics realization of a recent suggestion by Spergel and Steinhardt that collisional but dissipationless dark matter may resolve the core density problem in dark matter-dominated galaxies such as the dwarf galaxies. The realization is the asymmetric mirror universe model introduced to explain the neutrino puzzles and the microlensing anomaly. The mirror baryons are the dark matter particles with the desired properties. The time scales are right for resolution of the core density problem and formation of mirror stars (MACHOs observed in microlensing experiments). The mass of the region homogenized by Silk damping is between a dwarf and a large galaxy.