The dynamical and physical properties of asteroids offer one of the few constraints on the formation, evolution, and migration of the giant planets. Trojan asteroids share a planet's semimajor axis but lead or follow it by about 60° near the two triangular Lagrangian points of gravitational equilibrium. Here we report the discovery of a high-inclination Neptune Trojan, 2005 TN53. This discovery demonstrates that the Neptune Trojan population occupies a thick disk, which is indicative of ``freeze-in'' capture instead of in situ or collisional formation. The Neptune Trojans appear to have a population that is several times larger than the Jupiter Trojans. Our color measurements show that Neptune Trojans have statistically indistinguishable slightly red colors, which suggests that they had a common formation and evolutionary history and are distinct from the classical Kuiper Belt objects.