We investigate several strong spin-orbit coupling ternary chalcogenides related to the (Pb,Sn)Te series of compounds. Our first-principles calculations predict the low-temperature rhombohedral ordered phase in TlBiTe₂, TlBiSe₂, and TlSbX₂ (X=Te, Se, S) to be topologically nontrivial. We identify the specific surface termination that realizes the single Dirac cone through first-principles surface state computations. This termination minimizes effects of dangling bonds, making it favorable for photoemission experiments. In addition, our analysis predicts that thin films of these materials could harbor novel 2D quantum spin Hall states, and support odd-parity topological superconductivity.