High-performance thermoelectric materials require high-symmetry crystal structures that have large band degeneracies to yield good electronic properties. However, most of the semiconductors in nature possess low-symmetry crystal structures. In this study, the authors demonstrate a successful example of a high-performance thermoelectric material from a family of low-symmetry noncubic quaternary chalcopyrites. Three novel quaternary tetragonal chalcopyrites Cu2TMSnSe4 (TM = Mn, Fe, Co) have been selected based on their structure distortion parameters close to unity. This gives rise to a pseudocubic structure containing an inherently long-range cubic-like framework and localized lattice distortions. Thermoelectric properties of Cu2TMSnSe4 (TM = Mn, Fe, Co) from 300 to 850 K have been systematically investigated. Large Seebeck coefficients, moderate electrical conductivities, and high power factors are observed in these chalcopyrites, which are attributed to their high band degeneracies caused by the cubic-like cation framework. Meanwhile, the locally distorted noncubic anion frameworks lead to a low lattice thermal conductivity in Cu2TMSnSe4 (TM = Mn, Fe, Co). Consequently, high thermoelectric figures of merit with a maximum value of about 0.7 at 850 K have been achieved in these materials, representing some of the best values seen in quaternary chalcopyrites.