The synthesis, structure, and band structure analysis of the quaternary compound K0.33Ba0.67AgTe2 are reported. Crystals of K0.33Ba0.67AgTe2 were obtained in a K2Te/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 degrees C for 3 days followed by a slow cooling to 150 degrees C. The compound has a substructure in the tetragonal spade group I4/mmm (no. 139) with a(sub) = 4.624(2) Angstrom, c(sub) = 23.326(4) Angstrom, V = 498.7(3) Angstrom 3, at 20 degrees C (Mo K alpha radiation) : Z = 4, D-calc, = 6.23 g/cm(3), 2 theta(max), = 50 degrees, data collected : 592, independent data : 172, observed with I > 3 sigma(I) : 108, variables : 13, final R = 0.054, R(w) = 0.067. K0.33Ba0.67AgTe2 has a lamellar structure related to that of Na1.9Cu2Se2Cu2O. The substructure contains a readily recognizable [Te-2](4/3-) square net. The closest Te-Te distance in the net is 3.269(2) Angstrom, not a full covalent bond, but too shea for a simple van der Waals contact. While it is predicted that the square [Te-2](4/3-) 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 a(super) = 2.84a(sub), b(super) = b(sub), and c(super) = c(sub), and a commensurate tetragonal superstructure with a(super) = 3a(sub), b(super) = 3b(sub), and c(super) = c(sub). Both extended-Huckel and Huckel calculations suggest that this distortion is a charge density wave. In the case of the incommensurate cell, the theoretically predicted supercellcorresponds to the experimentally observed. We also used the mu 2-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.