We study the impact of the capture and annihilation of weakly interacting massive particles (WIMPs) on the evolution of Population III stars. With a suitable modification of the Geneva stellar evolution code, we study the evolution of 20 and 200M{sub {center_dot}} stars in dark matter halos with densities between 10{sup 8} and 10{sup 11} GeV/cm{sup 3} during the core H-burning phase, and, for selected cases, until the end of the core He-burning phase. We find that for WIMP densities higher than 5.3 10{sup 10}({sigma}{sub p}{sup SD}/10{sup -38} cm{sup 2}){sup -1} GeV cm{sup -3} the core H-burning lifetime of 20M{sub {center_dot}} and 200M{sub {center_dot}} stars exceeds the age of the Universe, and stars are sustained only by WIMP annihilations. We determine the observational properties of these 'frozen' objects and show that they can be searched for in the local Universe thanks to their anomalous mass-radius relation, which should allow unambiguous discrimination from normal stars.