The new BaTl3 compound has been synthesized and characterized by physical property measurements and electronic structure calculations. Its structure (Cmcm) is a new intermediate in the Ni3Sn family (P6(3)/mmc), and consists of thallium layers formed from two-center bond formation between the parallel chains of face-sharing octahedral clusters. The valence electron concentration (VEC) of the thallium layers is consistent with their two-dimensional nature, in comparison with those in other AX(3)-type compounds with one- or three-dimensional anionic networks with the same building blocks and different VECs. The unique geometric features of the anionic thallium layers bring on an unusual competition between inter-and intracluster bonds. Detailed studies of the energetics of BaTl3 reveal for the first time the important role of cation-anion interactions in the bonding competition in such an anionic substructure.