Single crystals of Ba2ZnQ3 (Q = Se, Te) were obtained by solid-state reactions at 1173 K. These isostructural compounds crystallize in the K2AgI3 structure type. The Zn atoms in this structure are coordinated to four Q atoms (2 Q1, 1 Q2, 1 Q3) and these form a distorted tetrahedron around each Zn atom. Each ZnQ4 tetrahedron shares two corners with neighboring ZnQ4 tetrahedra resulting in the formation of infinite chains of [ZnQ44-] units. The absorption spectrum of a single crystal of Ba2ZnTe3 shows an absorption edge at 2.10(2) eV, consistent with the darkred color of the crystals. From DFT calculations Ba2ZnSe3 and Ba2ZnTe3 are found to be semiconductors with electronic band gaps of 2.6 and 1.9 eV, respectively.