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ACrX2 (A = Cu, Ag; X = S, Se) compounds have a layered triangular structure similar to that of delafossites. In addition to a large variety of physical and chemical properties found in centrosymmetric delafossites, the broken inversion symmetry along the c-axis in this system leads to the emergence of additional functionalities such as piezoelectric, pyroelectric, and/or nonlinear optical properties. We found that the chemical vapor transport (CVT) technique using CrCl3 was the best growth method for ACrX2. In the case of A = Cu, however, a standard CVT procedure always produced a certain amount of a secondary phase, identified as the CuCr2X4 spinel, which significantly affected magnetic and transport properties. By a modified CVT technique with appropriate heat treatments, pure single crystals of CuCrX2 were successfully grown. The resistivity of ACrX2 was systematically changed by the combinations of A and X atoms. In contrast to metallic selenides, sulfides were confirmed to be insulators with giant anisotropy (10² ≈ 10³) between the out-of-plane (c-direction) and the in-plane (ab-plane) resistivity. In both X = S and Se, resistivity for A = Ag was higher than that for A = Cu. The drastic change in resistivity without carrier doping suggests that ionic conductivity and strong electron correlations play an important role in these materials. [ABSTRACT FROM AUTHOR]