Microquasars are binary star systems with relativistic radio-emitting jets. They are potential sources of cosmic rays and can be used to elucidate the physics of relativistic jets. We report the detection of variable gamma-ray emission above 100 gigaelectron volts from the microquasar LS I +61 303. Six orbital cycles were recorded. Several detections occur at a similar orbital phase, which suggests that the emission is periodic. The strongest gamma-ray emission is not observed when the two stars are closest to one another, implying a strong orbital modulation of the emission or absorption processes.