We discuss the possibility of a multidimensional structure of inhomogeneous chiral condensates, which might be realized in cold and dense quark matter or the core of compact stars. For one-dimensional structures, the system becomes unstable at finite temperature due to the Landau-Peierls instability attributed to the excitation of the Nambu-Goldstone modes, with the result that there is no long-range order, while quasi-long-range order is realized instead. On the other hand, chirally inhomogeneous phases with two- or three-dimensional modulations may be realized as a true long-range ordered phase at any temperature, as inferred from the Landau-Peierls theorem. We here consider possible strategies to explore a multidimensional structure of chiral crystals.