CuBiP2Se6, AgBiP2Se6, and AgBiP2S6 were prepared from the corresponding elements. CuBiP2Se6 and AgBiP2Se6 crystallize in the space group R (3) over bar with a = 6.5532(16) angstrom and c = 39.762(13) angstrom for CuBiP2Se6 and a = 6.6524(13) angstrom and c = 39.615(15) angstrom for AgBiP2Se6. AgBiP2S6 crystallizes in the triclinic space group P (1) over bar with a = 6.3833(13) angstrom, b = 7.1439(14) angstrom, c = 9.5366(19) angstrom, alpha = 91.89(3)degrees, beta = 91,45(3)degrees, gamma = 94.05(3)degrees. CuBiP2Se6 was found to exhibit a temperature-dependent antiferroelectric ordering of the Cu+ and Bi3+ ions in the lattice. An intermediate and a fully ordered structure were refined at 173 and 97 K, respectively. Electronic band and total energy calculations at the DFT level clearly suggest that the antiferroelectric model is energetically favored over the paraelectric and hypothetical ferrielectric models. This phase transition can be classified as a second-order Jahn-Teller distortion. The antiferroelectric state of CuBiP2Se6 is an indirect gap semiconductor. The compounds were characterized with differential thermal analysis and solid-state UV/vis diffuse reflectance spectroscopy. Generalized implications regarding the expected ferroelectric behavior of compounds in the CuMP2Se6 System (M = trivalent metal) are discussed.