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A novel cooling mechanism is proposed for neutron stars, based on the recentdevelopment in the studies of the QCD phase diagram. Possible appearance of theinhomogeneous chiral phase makes the quark beta decay without gluonicinteraction. An estimate of the neutrino emissivity shows the order of$10^{24-26}(T/10^9)^6$(erg cm$^{-3}$ s$^{-1}$) near the phase boundaries, whoseefficiency is comparable with the usual quark cooling or pion cooling, but itworks only in the limited density region. These features may give anothercooling scenario of neutron stars.

Quark beta decay in the inhomogeneous chiral phase and cooling of compact stars