The synthesis, structure, and band structure analysis of the quaternary compound &.33Ba067AgTe2 are reported. Crystals of Ko.aBa0.67AgTe2 were obtained in a KzTe/BaTe/Te flux by the reaction of 1 mmol of K2Te, 0.5 mmol of BaTe, 0.5 mmol of Ag, and 4 mmol of Te in an evacuated Pyrex tube at 450 OC for 3 days followed by a slow cooling to 150 OC. The compound has a substructure in the tetragonal space group Z4/mmm (no. 139) with asub = 4.624(2) A, Csub = 23.326(4) A, v = 498.7(3) A3, at 20 oc (MO K a radiation): z = 4, ~~~l~ = 6.23 g/cm3, 2&,, = 50°, data collected: 592, independent data: 172, observed with Z > 3a(I): 108, variables: 13, final R = 0.054, R, = 0.067. Ko.33Bao.67AgTe2 has a lamellar structure related to that of Na1.9Cu2Se2Cu20. The substructure contains a readily recognizable [Te~l"~square net. The closest Te-Te distance in the net is 3.269(2) A, not a full covalent bond, but too short for a simple van der Waals contact. While it is predicted that the square [Te2I4"net has metallic properties, the experimental data show a semiconductor behavior which has its origins in a structural distortion. Electron diffraction measurements reveal the presence of two different but related superstructures; an incommensurate orthorhombic superstructure of the tetragonal cell with asuper = 2.84asub, bsuper = bsub, and Csuper = Csub, and a commensurate tetragonal superstructure with asuper =3asub, bsuper = 3bsub, and csuper = Csub. Both extendedHuckel and Huckel calculations suggest that this distortion is a charge density wave. In the case of the incommensurate cell, the theoretically predicted supercell corresponds to the experimentally observed. We also used the p2-scaled Huckel method to predict the actual atomic positions within the supercell. The theoretically predicted superstructures have calculated diffraction patterns similar to the experimentally observed ones.