The economic damage caused by episodic outbreaks of forest-defoliating insects has spurred much research, yet why such outbreaks occur remains unclear. Theoretical biologists argue that outbreaks are driven by specialist pathogens or parasitoids, because host-pathogen and host-parasitoid models show large-amplitude, long-period cycles resembling time series of outbreaks. Field biologists counter that outbreaks occur when generalist predators fail, because predation in low-density defoliator populations is usually high enough to prevent outbreaks. Neither explanation is sufficient, however, because the time between outbreaks in the data is far more variable than in host-pathogen and host-parasitoid models, and far shorter than in generalist-predator models. Here we show that insect outbreaks can be explained by a model that includes both a generalist predator and a specialist pathogen. In this host-pathogen-predator model, stochasticity causes defoliator densities to fluctuate erratically between an equilibrium maintained by the predator, and cycles driven by the pathogen. Outbreaks in this model occur at long but irregular intervals, matching the data. Our results suggest that explanations of insect outbreaks must go beyond classical models to consider interactions among multiple species.