The single crystals of a quaternary sulfide, Ba₄FeAgS₆, have been synthesized by reacting elements at 873 K inside a sealed fused silica tube. The title phase is the first ordered quaternary compound of the Ba–Ag–Fe–S system. The crystal structure of Ba₄FeAgS₆ is characterized by a single-crystal X-ray diffraction study at 298(2) K. It crystallizes in the space group C⁵_2h – P2₁/n of the monoclinic crystal system with unit cell dimensions of a = 8.6367(5) Å, b = 12.0291(7) Å, c = 13.2510(7) Å, and β = 109.015(2)°. This compound is stoichiometric, and its structure contains twelve unique crystallographic sites: four Ba, one Fe, one Ag, and six S sites. All atoms of the structure occupy the general positions. The Ba₄FeAgS₆ structure consists of one-dimensional chains of ¹_∞[FeAgS₆]⁸⁻ that are extended in the [100] direction. The negative charges on these chains are counterbalanced by the filling of Ba²⁺ cations in between the ¹_∞[FeAgS₆]⁸⁻ chains. The Fe atoms are bonded to four S atoms that form a distorted tetrahedral geometry around the central Fe atom. Each Ag atom in this structure is coordinated with four S atoms in a distorted tetrahedral fashion. These FeS₄ and AgS₄ motifs are the main building blocks of the Ba₄FeAgS₆ structure. The corner-sharing of FeS₄ and AgS₄ tetrahedra creates one-dimensional chains of ¹_∞[FeAgS₆]⁸⁻. This structure does not contain any homoatomic or metallic bonds and can be charge-balanced as (Ba²⁺)₄(Fe³⁺)₁(Ag¹⁺)₁(S²⁻)₆. The optical absorption study performed on a polycrystalline Ba₄FeAgS₆ sample reveals a direct bandgap of 1.2(1) eV. The magnetic studies reveal the antiferromagnetic behavior of Ba₄FeAgS₆ below 50 K. The thermal conductivity and theoretical electronic structure of Ba₄FeAgS₆ are also studied in detail.