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Delafossite crystals are fascinating ternary oxides that have demonstrated transparent conductivity and ambipolar doping. Here we use a high-throughput approach based on density functional theory to find delafossite and related layered phases of composition ABX2, where A and B are elements of the periodic table, and X is a chalcogen (O, S, Se, and Te). From the 15 624 compounds studied in the trigonal delafossite prototype structure, 285 are within 50 meV/atom from the convex hull of stability. These compounds are further investigated using global structural prediction methods to obtain their lowest-energy crystal structure. We find 79 systems not present in the materials project database that are thermodynamically stable and crystallize in the delafossite or in closely related structures. These novel phases are then characterized by calculating their band gaps and hole effective masses. This characterization unveils a large diversity of properties, ranging from normal metals, magnetic metals, and some candidate compounds for p-type transparent electrodes.