A new quaternary sulfide telluride, Ba6Fe2Te3S7, was synthesized by a solid-state reaction, and its crystal structure is novel. X-ray diffraction data on powder and single crystals reveal an orthorhombic lattice with a = 9.7543(3) Å, b = 18.2766(6) Å, and c = 12.0549(4) Å, and the noncentrosymmetric space group Cmc21 (No. 36). The properties of the compound were studied by magnetic susceptibility investigations, specific heat measurements, Mössbauer spectroscopy, and density functional theory calculations. Assuming Ba2+ and, as verified by the Mössbauer spectra, Fe3+, the charge balance requires the presence of a polytelluride, suggested to be a straight-chain [Te34-] polyanion. Further, the crystal structure contains [Fe2S7]8- dimers of two vertex-sharing tetrahedra, with a nearly linear Fe-S-Fe atom arrangement. The dimer exhibits antiferromagnetic coupling, with a coupling constant J = -10.5 meV (H = -2JS1S2) and S = 5/2, resulting in a spin singlet ground state. The interdimer magnetic interaction is so weak that the magnetic dimers can be treated as individuals.