Ba2Cu6-xSTe4 and Ba2Cu6-xSeyTe5-y were prepared from the elements in stoichiometric ratios at 1123 K, followed by slow cooling. These chalcogenides are isostructural, adopting the space group Pbam (Z = 2), with lattice dimensions of a = 9.6560(6) angstrom, b = 14.0533(9) angstrom, c = 4.3524(3) angstrom, and V = 590.61(7) angstrom(3) in the case of Ba2Cu5.53(3)STe4. A significant phase width was observed in the case of Ba2Cu6-xSeyTe5-y with at least 0.17(3) <= x <= 0.57(4) and 0.48(1) <= y <= 1.92(4). The presence of either S or Se in addition to Te appears to be required for the formation of these materials. In the structure of Ba2Cu6-xSTe4, Cu-Te chains running along the c axis are interconnected via bridging S atoms to infinite layers parallel to the a,c plane. These layers alternate with the Ba atoms along the b axis. All Cu sites exhibit deficiencies of up to 26%. Depending on y in Ba2Cu6-xSeyTe5-y, the bridging atom is either a Se atom or a Se/Te mixture when y <= 1, and the Te atoms of the Cu-Te chains are partially replaced by Se when y > 1. All atoms are in their most common oxidation states: Ba2+, Cu+, S2-, Se2-, and Te2-. Without Cu deficiencies, these chalcogenides were computed to be small gap semiconductors; the Cu deficiencies lead to p-doped semiconducting properties, as experimentally observed on selected samples.