A new series of metal chalcogenides with the formula Ba6Ag2.67+4δSn4.33-δS16-xSex (x = 0 for 1, x = 6.47 for 2, and x = 16 for 3) were synthesized. Compounds 1-3 are isotypic with a three-dimensional structure and crystallize in the noncentrosymmetric space group I4¯3d. The framework in 1 is constructed by alternative corner-sharing of AgS4 and SnS4 tetrahedra with Ba2+ cations distributed within the channels. The Ag+ atoms are disordered with two neighboring silver sites trapped in various coordination environments. Selected area electron diffraction (SAED) patterns from samples of 1 indicate that the structural lattice is ordered without evidence of long-range ordering. High resolution electron microscopy (HREM) images of 1 along the  direction display the body-centered arrangement of barium atoms and the periodic appearance of lines between barium atoms that correspond to part of the array of disordered silver atoms. Within the sulfide composition range, the solid solutions are Ba6Ag2.67+4δSn4.33-δS16 with δ = 0.13 for 1, 0.31 for 1a, and 0.33 for 1b; the crystal colors range from dark-red to orange and yellow, respectively. All compounds are transparent in the mid-infrared region and have absorption edges ranging from 1.27 to 2.37 eV. The significant second harmonic generation (SHG) intensities of the five materials are optimized at wavelengths ranging from 600 to 800 nm. The outstanding ones are 1a and 2 which display strong intensities 4.4-11.6 times and 2.2-10.4 times that of AgGaSe2 in the ranges 600-700 nm and 675-800 nm, respectively. Raman spectroscopic characterization is reported.