Millisecond pulsars, old neutron stars spun up by accreting matter from a companion star, can reach high rotation rates of hundreds of revolutions per second. Until now, all such "recycled" rotation-powered pulsars have been detected by their spin-modulated radio emission. In a computing-intensive blind search of gamma-ray data from the Fermi Large Area Telescope (with partial constraints from optical data), we detected a 2.5-millisecond pulsar, PSR J1311-3430. This unambiguously explains a formerly unidentified gamma-ray source that had been a decade-long enigma, confirming previous conjectures. The pulsar is in a circular orbit with an orbital period of only 93 minutes, the shortest of any spin-powered pulsar binary ever found.