We have performed angle-resolved photoemission spectroscopy on TlBiSe₂, which is a member of the ternary chalcogenides theoretically proposed as candidates for a new class of three-dimensional topological insulators. We found direct evidence for a nontrivial surface metallic state showing an "X"-shaped energy dispersion within the bulk-band gap. The present result unambiguously establishes that TlBiSe₂ is a strong topological insulator with a single Dirac cone at the Brillouin-zone center. The observed bulk-band gap of 0.35 eV is the largest among known topological insulators, making TlBiSe₂ the most promising material for studying room-temperature topological phenomena.