In many complex systems, large events are believed to follow power-law, scale-free probability distributions, so that the extreme, catastrophic events are unpredictable. Here, we study coupled chaotic oscillators that display extreme events. The mechanism responsible for the rare, largest events makes them distinct and their distribution deviates from a power-law. Based on this mechanism identification, we show that it is possible to forecast in real time an impending extreme event. Once forecasted, we also show that extreme events can be suppressed by applying tiny perturbations to the system.