We have trapped a gas of long-lifetime, high-mobility excitons in an in-plane harmonic potential. Trapping is an important step toward the goal of a controlled Bose-Einstein condensate of excitons. We show that the repulsive interaction between the excitons plays a dominant role in the behavior of the excitons, in contrast with the weak interactions in atomic gases. We show that under proper conditions the excitons thermalize in the trap to a well-defined equilibrium spatial distribution.