A Toroidal Alfven eigenmode (TAE) has been observed to be driven by alpha particles in a JET deuterium-tritium internal transport barrier plasma. The observation occurred 50ms after the removal of neutral beam heating (NBI). The mode is observed on magnetics, soft-xray, interferometry and reflectometry measurements. We present detailed stability calculations using a similar tool set validated during deuterium only discharges. These calculations strongly support the conclusion that the observed mode is a TAE, and that this mode was destabilized by alpha particles. Non-ideal effects from the bulk plasma are interpreted as responsible for suppressing the majority of TAEs which were also driven by alpha particles, but the mode that matches the observations is predicted to be exceptional in the weakness of these non-ideal effects. This mode that is located far from the core on the outboard midplane is found to be driven by the precessional motion of large trapped alpha-particle orbits, despite alpha particles originating in the core.