Single crystals of the ternary copper compounds CuTlS and CuTlSe have been successfully grown from stoichiometric melt by using vertical Bridgman-Stockbarger method. The crystal structure of the both compounds has been determined by powder and single crystal X-Ray diffraction. They crystallize in the PbFCl structure type with two formula units in the tetragonal system, space group P4/nmm, а=3.922(2); c=8.123(6); Z=2 and а=4.087(6); c=8.195(19) Å; Z=2, respectively. The band structure of the reported compounds has been analyzed by means of full-potential linearized augmented plane-wave (FLAPW) method based on the density functional theory (DFT). Both compounds have similar band structures and are narrow-gap semiconductors with indirect band gap. The resistivity measurements agree with a semiconductor behavior although anomalies are observed at low temperature.