A crewman on a commercial tuna-fishing boat was the first to spot it: something shiny and metallic in the water off the ship's bow. The crewman alerted the navigator, and the 280-foot San Nikunau slightly altered course to avoid a collision. As the ship came closer, the object revealed itself to be a small boat, an aluminum dinghy. It was late in the afternoon on November 24 of last year. The New Zealand–based San Nikunau was in open water, a couple of days out of Fiji, amid the vastness of the southern Pacific—an expanse the size of a dozen Saharas in which there are only scattered specks of land.

The dinghy, fourteen feet long and low to the water, was designed for traveling on lakes or hugging a shoreline. There was no way it should've been in this part of the Pacific. If the San Nikunau had passed a quarter mile to either side, likely no one would have noticed it. Anyway, it appeared empty, another bit of the ocean's mysterious flotsam. But then, as the big ship was approaching the dinghy, something startling happened. From the bottom of the tiny boat, emerging slowly and unsteadily, rose an arm—a single human arm, skinny and sun-fried and waving for help.

There were, as it turned out, three people on the boat. Three boys. Two were 15 years old and the third was 14. They were naked and emaciated. Their skin was covered with blisters. Their tongues were swollen. They had no food, no water, no clothing, no fishing gear, no life vests, and no first-aid kit. They were close to death. They had been missing for fifty-one days.

It began, in the grand tradition of ill-considered ideas, with a group of boys and a bottle of booze—the most common of circumstances in the least common of places. The boys were gathered in their clubhouse—broken sofas, graffitied walls—near the end of the only road in the only village on the Pacific island of Atafu. Atafu is one of three atolls that make up the nation of Tokelau (which is not, technically, a nation but a territory of New Zealand). The total amount of land on Atafu is 1.4 square miles. Population: 524.

The nearest atoll, equally tiny, is fifty-seven miles to the south, well beyond the range of visibility. The closest significant land mass is Samoa, a twenty-eight-hour ferry ride away. There is no landing strip on Tokelau. There are also no dogs, prisons, lawyers, pavement, or soil—the land is mostly bits of broken coral. The highest elevation is fifteen feet. Coconuts and fish are the traditional diet, though the ferry, which comes once every two weeks, brings so much junk food these days that obesity and diabetes have become significant problems. From any point on Atafu's shoreline, nothing can be seen but water, all the way to the horizon.

One of the boys in the clubhouse—by most accounts, the unofficial leader—was named Filo Filo. (It's not uncommon in Tokelau to have the same first and last names.) Filo was tall and strong and exceptionally athletic. His dream was to play for the New Zealand All Blacks. Though his parents were both Tokelauan, Filo had lived his entire life away from the islands, mostly in Sydney, Australia, where his mother had moved after she'd separated from Filo's father. But in 2007, Filo's mother grew concerned about his poor grades and growing reputation as a troublemaker. As a sort of reform school, she sent him to Atafu to live with his dad, who in addition to being a fisherman—the profession of nearly every Tokelauan man—was also the local rugby coach. Filo became a star athlete on Atafu, but some people still thought of him, to use the Tokelauan word, as a palagi—a foreigner. One classmate called him a "wanna-be gangster." He was, in truth, a city kid who had been exiled to one of the tiniest and most remote places on the planet.

Filo had become best friends with a boy named Samu Tonuia. They were both 15 and in the same class at school—a class of seven students. Samu, like Filo, was tall and muscular for his age and also an excellent rugby player. Otherwise, the two boys could not have been more different. Samu had never once in his life left Tokelau. It is customary in Tokelau to assign one child to care for elderly relatives, and while the rest of his family had moved to Australia, Samu lived on Atafu with his grandmother. He'd never been in an airplane or a restaurant or a movie theater. According to one classmate, Samu had been a decent student—until Filo arrived.

So there they were, Filo and Samu, the permanent foreigner and the ultimate local, a gang of two, sitting in their clubhouse along with a handful of other boys. It was October 3, 2010. They were drinking vodka, smoking cigarettes, telling stories. It was getting late.

Then someone brought up the tale of the teenagers. Five or six years previous, three teens had taken a boat without permission and broken one of the cardinal rules of Tokelauan society: They'd ventured into the open ocean without the escort of a tautai, a master fisherman. Atafu's forty-two small islands encircle a gorgeous turquoise lagoon in which anyone can boat or swim. It's the kiddie pool. The ocean is an unpredictable and occasionally violent place, and the title of tautai, bestowed by the island's elders, is equivalent to a driver's license. Even tautais do not venture far offshore.

But to teenage boys, in Atafu as in every pocket of the planet, rules are made to be broken. And the isolation of Atafu can at times be difficult to bear. There's now satellite Internet service on the island, which only emphasizes how much fun everyone else is having. Filo told me that Atafu "felt like a prison." The desire to escape can become overwhelming.

Which is what those teenagers did five or six years ago. They escaped, trying to reach some other place. Any other place. They didn't make it. They were rescued after five days by the Tokelau ferry. They'd run out of gas but had plenty of food. Though they were severely punished by the elders, in Filo and Samu's clubhouse they were heroes. And as a plastic jug of vodka was passed around, the old story soon morphed into a new idea. By the time the jug was finished, the idea had become a plan.