(FORTUNE Magazine) – I'll admit it. Ever since watching Gilligan's Island, I've had a secret fantasy. (No, it has nothing to do with Tina Louise.) I've dreamed of being marooned on a tropical island--draped in palm fronds, drenched in the equatorial sun, loitering endlessly on the virgin white sand. Until suppertime.

That right there is the problem with escapist fantasies: It's all fun and games until someone gets hungry. Fortunately for that not-so-rare breed of traveler--the isolationist who likes to eat really, really well--there's Cayo Espanto. In the warm turquoise waters of the western Caribbean, just off Belize's great barrier reef, this relatively new private-island resort lets you glide effortlessly between playing castaway Gilligan and face-stuffing Henry VIII.

Of course, one has to get there first. And the easiest way, it seems, is by shipwreck. My wife's and my journey began at 6:30 A.M. in New York City, and after two long-delayed flights to the one-horse Belize International Airport, we hopped on a twin-engine prop plane for a dizzying 20-minute ride. Next we were rushed to a taxi and then to a speedboat, which whipped us through the narrow shoals in the dead of night to a dot of an island seven minutes away. We were waiting for a sherpa and a mule to lead us the rest of the way, but what greeted us instead was a torch-lit receiving line of smiling island staffers, dressed crisply in white polo shirts and khaki shorts.

At that point we realized, gratefully, that we were in for a good, solid pampering. Our enormous, high-ceilinged cabana, Casa Olita, was charmingly appointed with a sitting area, a kitchenette, and a sprawling bathroom (with a separate alfresco shower), as well as a cushy king-sized bed surrounded by mosquito netting. (Trust me, this billowy curtain, delicate as a bridal veil, is not for show.) On three sides the "walls" open up in the form of louvered sliding doors, letting the trade winds flood the room with gentle breezes and occasionally disorienting the mosquitoes. But what really caught our breath was what lay just feet beyond those doors: the sea. Each of the island's five cabanas is fronted by a covered deck and a freshwater plunge pool--and each has its own pier, replete with chaises longues, stretching into the crystal-clear Caribbean.

Within 30 minutes our gracious houseman Obed, a 24-year-old Belizean, was bringing us the first of our three dinner courses for that evening: pickled vegetable nori rolls with pineapple-tamari dipping sauce. Over the next four days chef Todd Unkefer--who had recently won a bronze medal in the respected Taste of Caribbean competition--never failed to surprise us. And most of the time, especially with his sopa azteca, roasted chicken with black bean muneta, and seared local grouper, he wowed us.

There is something odd about being served every meal in your room: After a while it feels vaguely like punishment. But the island is so tiny--just three acres, or less than a city block--that there isn't so much as a communal tiki bar at which to share a colada with other guests. Rather, Cayo Espanto--which means "phantom island"--is a place for would-be recluses.

Not to mention snorkelers and scuba divers. The resort comes with its own ever-accommodating dive master, who can not only expertly guide you through the famous Shark-Ray Alley at Hol Chan reserve, but ferry you to the nearby town of San Pedro if you get desperate for a crowd or a deep-sea fishing excursion.

As for my wife and me, our favorite daily routine was to kayak the placid, knee-deep water from one unpopulated island to the next. We'd sink our toes into untouched talcum beaches, scanning the tufts of palm trees for snowy egrets and heron. And then, after an hour or two of feeling like the only people on earth, we'd hurry back for dinner.