The reaction of Ag(NO3) with H3BO3 in oleum (20 % SO3) yielded single crystals of Ag[B(SO4)2] [tetragonal, P4/ncc, Z = 4, a = 8.6679(5) Å, c = 7.2897(5) Å, V = 547.69(7) Å3]. In Ag[B(SO4)2], infinite anionic chains, according to the Niggli formula ∞1[B(SO4)4/2]–, are found in tetragonal‐rod packing with charge compensation by AgI cations. The chains are built by central boron atoms coordinated through oxygen atoms to four bidentate bridging SO4 tetrahedra. Terminal oxygen atoms of the SO4 tetrahedra coordinate to the silver cations in the form of slightly distorted square prisms. Magnetochemical investigations reveal the expected closed‐shell behavior of d10 cations. DFT investigations of the solid‐state structure corroborate the experimental findings and permit the assignment of vibrational spectroscopic data.