The title compounds were prepared from the elements in evacuated silica tubes at 650 degrees C, followed by slow cooling. Ba2Ag4Se5 forms a new structure type, space group C2/m, with a=16.189(2) A, b=4.5528(6) A, c=9.2500(1) A, beta=124.572(3) degrees, and V=561.4(1) A3 (Z=2). A maximum of 44% of the Ag atoms may be replaced with Cu atoms without changing the structure type. The crystal structure is composed of Ag4Se(5)4- layers, interconnected via the Ba2+ cations. The Ag atoms show irregular [3+1] coordination by the Se atoms, and the Ba atoms are located in capped square antiprisms formed by Se atoms. Most intriguing is the unprecedented occurrence of linear Se(3)4- units. According to the formulation (Ba2+)2(Ag+)4Se(3)4-(Se2-)2, this selenide is electron-precise with eight positive charges equalizing the eight negative charges. Electronic structure calculations indicated the presence of a band gap, as was experimentally confirmed: the electrical conductivity measurement revealed a gap of 0.6 eV for Ba2CuAg3Se5.