The electronic band structures of Ce 3 Te 4 have been studied using the first-principles density-functional theory calculations. It is found that the density of states of Ce 3 Te 4 has a very high delta-shaped peak appearing 0.21 eV above the Fermi level, which mainly comes from the f orbital electrons of the rare-earth element Ce. Using the simple theory proposed by Mahan and Sofo, ͓Proc. Natl. Acad. Sci. U.S.A. 93, 7436 ͑1996͔͒, we obtain an ideal value of zT= 13.5 for Ce 3 Te 4 at T = 1200 K, suggesting that the rare-earth chalcogenide Ce 3 Te 4 could be a promising high efficiency high temperature thermoelectric material.