Motivated by the recent "Cosmos Project" observation of dark-matter concentrations with no ordinary matter in the same place, we study the question of the existence of compact objects made of pure dark matter. We assume that the dark matter is neutralino, and compare its elastic and annihilation cross sections. We find that the two cross sections are of the same order of magnitude. This result has a straightforward and important consequence that neutralinos comprising a compact object can not achieve thermal equilibrium. To substantiate our arguments, by solving Oppenheimer-Volkoff equation we constructed a model of the star made of pure neutralinos. We explicitly showed that the condition for the thermal equilibrium supported by the Fermi pressure is never fulfilled inside the star. This neutralino state can not be described by the Fermi-Dirac distribution. Thus, a stable neutralino star, which is supported by the Fermi pressure, can not exist. We also estimated that a stable star can not contain more than a few percents of neutralinos, most of the mass must be in the form of the standard model particles.