Patrice Faye is standing on the west bank of Burundi's Rusizi River with binoculars raised to his eyes.

"Quatre metres," the 52-year-old French expatriate says nonchalantly as he sizes up a 13-foot-long Nile crocodile basking on a sandbar 50 yards away. It's a wiltingly hot day at the end of the dry season in central Africa, and the muddy Rusizi, though diminished in height and volume, is still racing toward its rendezvous with Lake Tanganyika, a mile downstream. Faye has been studying Burundi's crocodiles for two decades and has seen countless individuals of this size. The bull is about 25 years old and weighs roughly 500 pounds—just average for a young adult male of the species, yet still capable of inflicting tremendous harm on man or beast.

This croc isn't the creature that Faye is looking for, however. Like Captain Ahab, the self-taught naturalist is preoccupied with one monster in particular: Gustave, the largest, most fabled crocodile in all of Africa—a demonic Loch Ness Monster of incredible proportions and, according to legend, appetite. Gustave is reputed to have devoured hundreds of villagers, snatching them from the banks of the Rusizi and the northeastern shores of Lake Tanganyika. Faye estimates that the massive croc measures 20 feet long, weighs one ton, and is 60 years old (wild crocs, on average, live to age 45). Trained herpetologists agree that Gustave could be that large and that he is certainly one of the most infamous man-eaters of all time. But Faye's assertion that Gustave kills for sport—knocking off villager after villager like some killing machine—leaves skeptics clearing their throats.

I've come to Burundi to suss out the myths and realities surrounding Gustave, and, hopefully, to document the end of his alleged bloody rampage. With me are photographer Bobby Model and French film director Vincent Munie. Along with Faye, an able storyteller who after six years of sleuthing knows more about Gustave than anyone, the three of us make up an advance search team. Our mission is to track down Gustave; he is still on the loose but has been sighted as recently as three weeks ago. We have five days to locate him before the arrival of our colleague Brady Barr, the world record holder for croc wrangling—3,000 captured in 15 years.