  In this paper, the question of the influence of color superconductivity (CSC)
on the formation of a phase with condensation of charged pions in dense
chirally asymmetric quark matter is studied. We consider it within the
framework of the massless NJL model with a diquark interaction channel at zero
temperature, but in the presence of baryon $\mu_B$, isospin $\mu_I$, chiral
$\mu_{5}$ and chiral isospin $\mu_{I5}$ chemical potentials. It has been shown
in the mean-field approximation that in the presence of chiral imbalance, when
$\mu_{5}\ne 0$ and/or $\mu_{I5}\ne 0$, CSC phenomenon does not hinder the
generation of charged pion condensation in dense quark matter even at largest
baryon densities attainable in heavy ion collisions experiments and in cores of
neutron stars and its mergers. So charged pion condensation in dense quark
matter with chiral imbalance predicted earlier is not in a bit suppressed by
the presence of CSC, highlighting the resilience of this phase in dense quark
matter. This makes phase structure of dense quark matter even more rich,
multifaceted and interesting, and shows that pion condensation in dense quark
matter is viable phenomenon to be explored, for example, in intermediate energy
heavy ion collisions experiments.
