  We investigate the surface state of Bi$_2$Te$_3$ using angle resolved
photoemission spectroscopy (ARPES) and transport measurements. By scanning over
the entire Brillouin zone (BZ), we demonstrate that the surface state consists
of a single non-degenerate Dirac cone centered at the $\Gamma$ point.
Furthermore, with appropriate hole (Sn) doping to counteract intrinsic n-type
doping from vacancy and anti-site defects, the Fermi level can be tuned to
intersect only the surface states, indicating a full energy gap for the bulk
states, consistent with a carrier sign change near this doping in transport
properties. Our experimental results establish for the first time that
Bi$_2$Te$_3$ is a three dimensional topological insulator with a single Dirac
cone on the surface, as predicted by a recent theory.
