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Three-dimensional topological insulators are a new state of quantum matter with a bulk gap and odd number of relativistic Dirac fermions on the surface. By investigating the surface state of Bi₂Te₃ with angle-resolved photoemission spectroscopy, we demonstrate that the surface state consists of a single nondegenerate Dirac cone. Furthermore, with appropriate hole doping, the Fermi level can be tuned to intersect only the surface states, indicating a full energy gap for the bulk states. Our results establish that Bi₂Te₃ is a simple model system for the three-dimensional topological insulator with a single Dirac cone on the surface. The large bulk gap of Bi₂Te₃ also points to promising potential for high-temperature spintronics applications.