  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 $\Gamma$ 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.
