As one might expect of a Bahamian tropical paradise, Blue Island abounds with powdery beaches and romantic coves, mango and banana trees, and miles of trails for hiking and biking. At the heart of this 700-acre idyll—the largest private island in the Bahamas—a gleaming white six-bedroom residence rises from a hilltop that reaches 90 feet above the sea.

But Blue Island (formerly known as both Innocence Island and Hog Cay) owes its allure to more than its serenity and size. “Blue is the only private island in the Bahamas with its own jet port,” said property manager Steve Donovan as our plane—a Cessna Citation—touched down lightly on the 5,700-foot-long landing strip and taxied to the far end of the runway. “The air field is built to accommodate planes up to the size of a business jet.”

Perhaps even more appealing is the fact that visitors to Blue, which is located among the many private islands in the exclusive Exumas chain, can clear customs right on the landing strip. Indeed, waiting to welcome us to the Bahamas was a customs and immigration official who stood by a second, smaller plane at the air field. Such a seamless journey is a rarity for a private island. “Your trip to other private islands may begin in a Falcon or G2,” Donovan said, “but to get where you’re going you have to transfer to a boat or ferry.”

The conveniences of a jet-accommodating air field and customs capabilities put many of the world’s potential private-island owners within easy reach. “We are just three hours from New York, five hours from Los Angeles, or eleven hours from Moscow,” Donovan said. “It makes Blue both the most exclusive and the most accessible private island in the Bahamas.”

What sets Blue apart, however, isn’t just what’s there, but what isn’t—tourists. “There is virtually no place you can go that has not been discovered or developed and turned into a mass-market destination,” Donovan said. “The only place to escape the tourists and paparazzi is a private island, where the ocean becomes a kind of moat.”

Thus the appeal of the Exumas for Johnny Depp, David Copperfield, Bernard Arnault, and the Aga Khan. “They are all fabulously rich, and they all own lavish hideaways in the Exumas. But no matter how wealthy they are, there’s one thing we have today that nobody else has.”

To be sure, Depp might be a celebrated movie star, but he can’t do with his private island what Donovan and I were doing—flying to Blue Island for lunch and returning to Palm Beach in time for afternoon cocktails. It was the kind of experience some might say money can’t buy. Except that now it can because Blue—beaches, docks, main house, observation towers, iguanas, air field, and all—is for sale for $125 million.

“This isn’t like real estate anywhere else in the world,” Donovan said. “You can’t compare comps, or even features and acreage, because this isn’t like any other place on Earth. It’s an event, a moment, an emotion, and bragging rights. It’s not just the biggest private island in the Bahamas, it’s also the most expensive.”