We predict a new class of three-dimensional topological insulators in thallium-based III-V-VI 2 ternary chalcogenides, including TlBiQ 2 and TlSbQ 2 (Q= Te, Se and S). These topological insulators have robust and simple surface states consisting of a single Dirac cone at the Γ point. The mechanism for topological insulating behavior is elucidated using both first-principle calculations and effective field theory models. Remarkably, one topological insulator in this class, TlBiTe 2, is also a superconductor when doped with p-type carriers. We discuss the possibility that this material could be a topological superconductor. Another material, TlSbS 2, is on the border between topological insulator and trivial insulator phases, in which a topological phase transition can be driven by pressure.