A mechanism is identified whereby dark matter (DM) in protostellar halos dramatically alters the current theoretical framework for the formation of the first stars. Heat from neutralino DM annihilation is shown to overwhelm any cooling mechanism, consequently impeding the star formation process and possibly leading to a new stellar phase. A "dark star" may result: a giant ( greater, similar 1 AU) hydrogen-helium star powered by DM annihilation instead of nuclear fusion. Observational consequences are discussed.