They come almost daily to see the Los Angeles house for sale on Bellagio Road.

They drive through the iron gates, up the sweeping driveway, past lofty pines, Doric pillars and a bronze boy who sits on a fountain.

A Saudi oil sheik comes one day, then the sister of the deposed shah of Iran, singer Barry White, another sheik, a record executive and then members of the Krupp family, the mumtions makers from Germany.

They come and they go. So far none of them has been willing to pay the price.

The price is $15 million.

"I don't know if we'll sell it at that price," said Donald Hubbs, the lawyer handling the sale. "To the right individual, it would be worth $15 million. But it's extremely difficult to find that individual. We're in no hurry. When you're selling a property of this dimension, you don't put it up as a fire sale."

The three-story home -- called Casa Encantada, the House of Enchantment -- is the Bel Air mansion of the late Conrad Hilton, the hotel tycoon who died this year at 91. And te price, which has caused a stir even in a neighborhood where million-dollar homes are common, is believed to be the highest ever set for a single-family dwelling anywhere.

"I can tell right away, when people come through the door," whether or not they're really potential buyers," said Hugo Mentz, the house's chief butler for 20 years. "Some people ask, 'How much does it cost to operate the house, how many servants do I really need?' If you ask that, this is not for you. You are nuts to think about buying."

What does $15 million buy these days?

The 64-room house, which sits on 8.34 heavily wooded acres and is enclosed on three sides by the fairways and greens of the exclusive Bel Air Country Club, has 23,506 square feet of living space, 10,000 square feet of patios and sundecks, 26 bathrooms, 16 bedrooms (all but five of which are for servants), four dumbwaiters, five kitchens, five wet bars and 12 fireplaces in different colors of marble.

It has a banquet room that seats 20 diners, a wine cellar built for 1,000 bottles, an intercom system with 26 stations, and a vault that stores enough silver trays, candelbra, sauce boats, pitchers, salt shakers and flatware to serve a gathering of 100.

And there is the view -- or more correctly the views, which on a clear day in winter include dozens of nearby million dollar estates, the skyline of downtown Los Angeles, the UCLA campus, the Pacific Ocean to the west and the snow-covered mountains to the east.

So much for the main house. The grounds also include an orchid house, another house for putting plants, a 2,000-square-foot guest house, numerous flower plots, a rose garden with 500 rosebushes, a badminton court that is being converted in to a putting green, and a two-bedroom doghouse with a copper roof (just like the main house) and a pantry, complete with a built-in can opener, where Fido's food can be prepared.

All of that is surrounded by a cyclone fence, intended neither to keep out burglars nor to mark the property line: It is there to prevent the deer that roam the hills of Bel Air from eating all the flowers.

Casa Encanada also has those two absolute necessities of Southern California life -- the swimming pool (with twin gazebos) and the tennis court (fully illuminable for night play, of course). And, in between is a 4,000-square-foot "recreation house," which has 16-foot-high ceilings (just like the main house).

But the real question is whether you are healthy enough even to rate a viewing. Hubbs, the Hilton family's longtime attorney, screens prospective buyers.

When a broker contacts him and asks him to have a client see the property, Hubbs demands a letter from the client stating that the broker actually does represent him plus some documentation that the individual could, if he chose, spend $15 million on a house. In the scramble for the commission on the place, several brokers have misrepresented themselves.

"Some wealthy people get insulted when I ask for the proof," Hubbs said. "They aren't used to being treated that way. I usually know who they are, but I also know that many wealthy people can't afford this house.

"It takes an extremely wealthy person. There aren't that many such people in the world. So much after-tax income is required just to run the place. We estimate operating costs at $400,000 to $500,000 a year. We don't want to disappoint a lot of people who are trying to make ends meet.

"Many people, I think, just want to see the house," Hubbs said, defending his screening. "That's not what we're here for. It takes two hours just to give a preliminary viewing."

Even a preliminary viewing doesn't provide enough time to appreciate the splendor of the bedroom for the lady of the house, where the walls, bedspreads and furniture are all done in gold-colored silk and the fireplace is made of green Italian marble.

It isn't long enough to savor the master suite, which includes bedroom, sitting room, dressing room bathroom, steamroom, Jacuzzi, sunlamp, shower and a giant tub with a seat built in at the back. All the fixtures are plated in 14-karat gold.

And unless the visitor lingers, he may miss some of the art objects that fill every corner of the house the 14th-century bronze statues of Devi and Siva from the south of India in the entrance hall; the black walnut walls of the banquet hall, inlaid with holly wood; the Ming vases from China in the foyer; the drawing-room panels painted in the 18th century by the French artist Jean Baptiste Huet; and in the powder room on the ground floor, a painted Moor, a lifesize, black-faced statue holding a sterling silver dish for cigarettes and cigars.

"The Hearst castle (200 miles up the California coast in San Simeon) doesn't compare," Hubbs said. "That's more of an art collection. This house was coordinated from the time of its inception."

Perhaps the most surprising thing about this collection of artistic goodies is that Conrad Hilton had nothing to do with it. All of it was in the house when he bought it from Hilda Boldt Weber in 1949. Hilton never touched a thing.

"Mr. Hilton was not an art collector," Mentz noted. "He collected hotels."

A house like Casa Encantada deserves a rich history, and happily, it has one.

The story begins with a man named Boldt who owned the Libbey-Owens glass company in Pittsburgh. Boldt was ill, and was brought back to health by an attentive nurse named Hilda, whom he subsequently married. They moved to Santa Barbara, Calif., where he soon died leaving much of his estate to his widow.

Hilda promptly married her butler, Otto Weber, and they decided to move to Los Angeles, reportedly because Santa Barbara society did not wholly approve of the marriage. She commissioned architect Mil Dolena to build them a home. But first she traveled to Europe, taking snapshots of the finest French Empire furniture she could find and upon her return, commissioned craftsmen to duplicate the furniture for her new home.

The house was built in 1938. The Webers lived there until 1949, when they sold it for $250,000 to Conrad Hilton, who was looking for a place where he could live and entertain comfortably. The Webers needed the money to pay off Hilda's gambling debts.

Hilton lived alone in the beige, H-shaped house, except for the small army of servants and guests, until he remarried in 1976.

So far, no one with "comfortable" money has stepped forward to claim the mansion as his own. Offers have been made but Hubbs has instructions not to bargain. Hilton's heirs are in no hurry to sell the estate; the money will go to charity. They are content to wait for their price.

". . . A house is not a painting to be hung in a gallery and admired," wrote Don May, the author of Hilton's book on the house. "It is more like a symphony score, a series of vertical and horizontal lines interwoven with symbols which rest dormant on a page until called to life by the interpretative genius Toscanini. A house must be lived in as a symphony must be played, and if its genius is great, it must have a maestro of hospitality to bring it to the fullness of life."

The search for the $15 million maestro goes on.