We have measured the differential cross section for the γHe3→π+t reaction. This reaction was studied using the Continuous Electron Beam Accelerator Facility (CEBAF) Large Acceptance Spectrometer (CLAS) at Jefferson Lab. Real photons produced with the Hall-B bremsstrahlung tagging system in the energy range from 0.50 to 1.55 GeV were incident on a cryogenic liquid 3He target. The differential cross sections for the γ3He→π+t reaction were measured as a function of photon-beam energy and pion-scattering angle. Theoretical predictions to date cannot explain the large cross sections except at backward angles, showing that additional components must be added to the model.