These pre-historic creatures can be found in a remote corner of Nepal, the inspiration for the fictional paradise of Shangri-La.
But the existence of these rhinos is in danger for two reasons. First, because poachers wants the rhino's horn, which is worth a small fortune on the black market. And second, because humans have been taking over their natural habitat, the primeval jungles of southern Nepal.
Only a few hundred of these ancient mammals survive today. And, as Correspondent Lara Logan reports, getting to them required a trek into a land that time forgot.
The rhinos live in the grasslands and rivers of Nepal's Chitwan National Park, and the safest way to get close to the two-ton beasts is on the back of an even bigger animal: an elephant.
More than a dozen highly trained elephants were waiting for us at the base camp, deep inside the park.
There, we joined up with the scientists and park rangers whose mission is to save the rhinos by learning more about how they live. They hunt them down, and then shoot them with special darts filled with a powerful tranquilizer.
Our hunting party was lead by Dr. Tirtha Maskey, director of Nepal's national parks. He has worked for 30 years to save rhinos from extinction.
Our first challenge was figuring out how to climb aboard the elephants. Biologist Eric Dinerstein gave us a quick lesson, and he's been doing this since he first came to Nepal in 1975 to study rhinos. Cameraman Dennis O'Keefe rode the elephant just ahead of us, as our caravan headed off into the bush.
Earlier this morning, Nepalese trackers were out on elephants and spotted two rhinos about a half-mile away. So that's where we're going -- into the world's tallest grassland, through a small patch of forest along the river. We hope to find the rhinos on the other side.
These rhinos live in the lowlands of Chitwan Park, which is 75 miles southwest of Kathmandu, on Nepal's border with India. The great one-horned rhinos are 15-foot-long behemoths with a pre-historic pedigree. They're fast, strong, and have razor-sharp teeth. And for 35 million years, they've lived in a primeval jungle alongside hundreds of other wild creatures.
What's so unique about these rhinos? "They're certainly very prehistoric looking. And their skin has been compared to armor plating because it's so thick it's got what look like little rivets on them. It's a rare glimpse on the past that we've lost in so many other places," says Eric Dinerstein, who's been going on these rhino hunts since 1985, when the World Wildlife Fund and the Nepalese government began trying to save animals on the edge of extinction.
In a bold experiment of conservation, scientists put tiny radio transmitters on the drugged rhinos and tracked them. Then, they moved a few to other national parks, and released them to start new rhino colonies. Today, there are more than 600 rhinos in Nepal.
But the struggle to save them is far from over. "I think it's gonna require, if not eternal vigilance, at least for the next 50 years," says Dinerstein.
Humans have been hunting rhinos in Nepal for centuries, but they used real guns with real bullets.
Nepal's royal family once hosted extravagant hunting parties, where the royal guests would slaughter rhinos and tigers by the dozens for souvenirs. Then the royal procession would head back to Kathmandu – the ancient capital of a remote and romantic kingdom.
Today, Kathmandu is still Nepal's capital, and it's almost as exotic as it was back then. Devout Hindus were cremating their dead on the banks of the river, scattering the ashes into the holy water. Buddhists were worshipping at the Monkey Temple, where these animals almost outnumber the monks.
There were trekkers and climbers from all over the world, drawn by the challenge of Mount Everest and the Himalayas. And there was even a polka-dotted elephant at the gates of Nepal's royal palace.
But there is a shadow over Shangri-la. Armed soldiers on the streets are one sign of an 8-year-long bloody insurrection, led by radical communists, which has claimed nearly 10,000 lives. The violence is at odds with this historically peaceful nation.
Our journey to see the rhinos took us through deep valleys and onto Nepal's southern plains. Along the way, we saw a country of great beauty, but one that is losing the battle against industrialization and poverty.
Poaching poses a direct threat to the rhinos, but it's a crime that pays well. "Its horn is valued, not as an aphrodisiac, which is a myth in the West, but really as an anti-fever agent," says Dinerstein. "And so, rhinos have really been persecuted for that reason.
Rhino horns confiscated from poachers are kept under lock and key at park headquarters. We looked at horns that would fetch about $30,000 each on the black market.
Soldiers are stationed in Nepal's parks to protect the animals from poachers. But some have been re-deployed to fight the insurgents, which makes it easier for the poachers.
The rhinos are also threatened by farmers, who have cleared most of the grasslands around Chitwan Park to plant rice and wheat -- squeezing out the rhinos.
As we were tracking those rhinos from the safety of our elephant's back, Dinerstein explained that the government now shares tourist dollars with the farmers to encourage them to share the land with big and wild rhinos.
"They're extremely dangerous animals. They do kill each other. They probably kill several people a year inside the park, who were trampled to death or gored," says Dinerstein.
What would you do if you were charged by a rhino?
"You'd probably want to run. The conventional wisdom is to rip off a piece of your clothing and drop it. And hopefully the rhino will become extremely interested in whatever you've left behind, and give you the opportunity to escape," says Dinerstein.
We follow a rhino trail that is commonly used while going through the grasslands. You can see three-toed, prehistoric tracks.
Suddenly, the rangers spot a rhino, but there's a problem. It's a mother and calf, and mothers with their young are typically more aggressive. The elephant drivers move to surround the female.
"This could be it. This should be exciting," says Dinerstein.
But the 2-year-old rhino calf proves to be unusually protective, and the elephants are surprisingly rattled. The first few tranquilizer darts didn't manage to penetrate the rhino, so the shooters maneuvered to get another shot. This time, the dart seems to take effect.
Dr. Maskey and his staff move quickly to make sure the rhino is indeed asleep, and in good health. Since this is the beginning of the hot season, they also put water on the rhino to keep its temperature steady.
Next, they have to move quickly to do their most important research task – to get the radio collar with a tiny transmitter around the rhino's neck. "By putting radio collars on them, one of the many pieces of information we can get on their private lives is how big a home range do they use," says Dinerstein.
Rhino horns are made of compressed hair, and Maskey showed Logan how vulnerable the horn is, even to normal wear-and-tear. But a damaged horn is still valuable to poachers.
Within 30 minutes, the researchers are finished and ready to wake the sleeping giant. "It went like clockwork. Everything that we wanted to do, we were able to do," says Dinerstein. "And now he's gonna inject the antidote in the ear veins, so we should probably get on the elephant fairly quickly, cause it could be on its feet."
60 Minutes II left a small camera on the ground to capture a moment not even the researchers get to see up close.
The rangers monitored the female rhino until she was reunited with her calf. Then, we headed back to the base camp. But as we prepared to leave Nepal and head for home, we're still in awe of these ancient beasts.
"I think there's something somewhat karmic about being next to these animals, that are at large and wild and leave footprints larger than our own," says Dinerstein. "And it teaches us a kind of humility that we lack."