Single-crystal and polycrystalline Ba4Cu8Se13 were synthesized; the average crystal structure was solved by single-crystal X-ray diffraction, and the structural model was confirmed by a detailed electron microscopy study of polycrystalline Ba4Cu8Se13. The title compound can be rationalized as (Ba2+)4(Cu+)8(Se2-)2(Se22-)4(Se34-) and crystallizes in a new structure type (space group C2/c with a = 9.171(8) Å, b = 9.146(8) Å, c = 27.35(3) Å, β = 93.21(3)°, and V = 2291 Å3). It contains unprecedented Cu4Se9 fragments with planar Cu rectangles. These fragments form two-dimensional layers via regular (2c-2e) Se-Se bonds. Two of these layers are then connected in the third dimension via linear, hypervalent Se34- units, resulting in "sandwichlike", layered building blocks, which are stacked along c and separated by Ba. Ba4Cu8Se13 is the first example where Se22- and Se34- groups coexist. We were able to visualize the crystal structure by recording HAADF images, which clearly reveal the Cu4Se9 fragments and linear Se34- units. The title compound is a charge-balanced semiconductor and possesses a large Seebeck coefficient (380 μV K-1 at 200 K) and a low thermal conductivity (0.77 W m-1 K-1 at 200 K)-two requirements for efficient thermoelectric materials.