  A new, gapless two-flavor color superconducting phase that appears under
conditions of local charge neutrality and $\beta$-equilibrium is revealed. In
this phase, the symmetry of the ground state is the same as in the conventional
two-flavor color superconductor. In the low-energy spectrum of this phase,
however, there are only two gapped fermionic quasiparticles, and the other four
quasiparticles are gapless. The origin and the basic properties of the gapless
two-flavor color superconductor are discussed. This phase is a natural
candidate for quark matter in cores of compact stars.
