  We investigate the effects of isospin asymmetry on the competition between
color-superconductivity and inhomogeneous chiral symmetry breaking in dense
two-flavor quark matter using an extended Nambu--Jona-Lasinio model. We confirm
the appearance of a coexistence window where chiral symmetry is inhomogeneously
broken and a nonzero spatially homogeneous diquark gap is present, consistently
with previous works, and show that such a phase survives at nonzero isospin
chemical potentials. We also discuss how the model phase structure becomes
modified as large isospin asymmetries are considered.
