  A novel cooling mechanism is proposed for neutron stars, based on the recent
development in the studies of the QCD phase diagram. Possible appearance of the
inhomogeneous chiral phase makes the quark beta decay without gluonic
interaction. 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, whose
efficiency is comparable with the usual quark cooling or pion cooling, but it
works only in the limited density region. These features may give another
cooling scenario of neutron stars.
