At a gate and guardhouse 18 miles from the reactor, cultivation stops entirely. Fields give way to forest, dark, fragrant, and still unsettling on my fourth visit in ten years to the exclusion zone, a tightly controlled area almost twice the size of Luxembourg. The first time, in 1995, a dog pranced up as I waited for guards to inspect my papers. I felt a stab of pity: A huge tumor had deformed its jaw. As the dog got closer, though, I realized that my anxiety about radioactivity had played a trick on me. The tumor was really a chunk of asphalt the dog was carrying in its mouth.

At the center of this accidental wilderness stands the sarcophagus, naval gray and malignant, and rustier than I remember. Built in six months, it was planned to last at most 20 years. One beam supporting the corrugated steel roof rests precariously on a severely damaged wall of the reactor hall, while the western side of the structure has bulged several inches. None of the joints were welded: Workers couldn't get close enough. Any of a number of freak scenarios—an earthquake, a tornado, a heavy snow—could bring it crashing down. Or the sarcophagus, also known as the shelter, could simply collapse on its own.

This fragile shelter holds an estimated 200 tons of nuclear fuel, some of it in the reactor core and some in an unearthly radioactive "lava"—fuel rods, concrete, and metal that melted together in the inferno and oozed into the warren of rooms beneath the reactor. There's enough enriched uranium and plutonium in the hulk for dozens of atomic bombs.

But the immediate threat is water. A few years ago workers measured more than a thousand square yards of cracks and holes in the sarcophagus, which were allowing rain and melted snow to pool in its bowels. The water further weakens the structure, and it seeps out into the environment, carrying radioactive contaminants. Water can also act as a nuclear moderator: a substance that aids a chain reaction. Though the risk is deemed minute, a renewed chain reaction could trigger another steam explosion, blowing open the sarcophagus, scattering chunks of fuel, and releasing tons of fine radioactive dust.

On the night of June 26, 1990, after two weeks of heavy rain, detectors in one lava-filled room registered a sharp rise in neutrons, a sign of an impending chain reaction. Four days later, a physicist from a technical center in the old town of Chernobyl, ten miles away, dashed in to pour neutron-quenching gadolinium nitrate on the lava. The neutrons subsided.

Similar selflessness over the years has taken a heavy toll. The technical center, run by the Ukrainian Academy of Sciences, is the home of the "stalkers," scientists who work in the sarcophagus, exposing themselves to high levels of radiation as they monitor the state of the reactor fuel. Near the entrance is a list of several dozen who have died, many in their 40s and 50s, many from cancer or heart disease. I recognize one, Edward Denisenko, whom I'd met a decade ago, and recall him musing about who in their right mind would want to work at Chernobyl. "If people from the West and Russia don't want to come here," he had asked, "who will? God? The devil?"