Not many people have heard about William Cushing "Billy" Paley, and he likes it that way.

"I've never had any publicity," says the only son of recently retired CBS board chairman William S. Paley and his socialite wife "Babe." Billy Paley was born in 1948 - the same year Jack Benny left NBC for CBS, a move that would entice more stars to join the fledging network Paley had acquired in 1928.

Twenty-nine years later, CBS ia a $2-billion conglomerate, William S. Paley has (partially) relinquished his throne and his son and heir - Vietnam veteran, filmmaker, ex-addict, college dropout, investor in the trendy Capitol Hill bar/restaurant The Gandy Dancer and self-exile from the glitter of his parents' New York social world - doesn't even watch television.

"I've tried to keep a very low profile," Paley says of his mildly rebellious background. Rejecting the sterility of posh New York drawing rooms for the comfort of a crash pad in the '60s was a luxury Paley, like many other sons and daughters of the rich, could easily afford. Now Paley has traded his life of leisure as well as his annonymity for the sake of business, 1977-style.

"All my life I've avoided exposure," Paley says. "When people ask me if I'm related to the New York Paley I say, 'No, Pele, the New York soccer player.' No one knows about me."

No wonder. The son of one of the richest and most powerful men in the world has been called "a hippie and a dropout" by author Robert Metz in "CBS: Reflections in a Bloodshot Eye" and in the words of his bemused benefactor, "a very unusual man."

"My father and I never really got along," Bill Paley says. "I was too weird for them to beleive. And of course I wasn't a success. I was different, that's all.I didn't want to alienate my parents. I love my parents, but I hated them, you know? I just left."

Bill Paley, 6 feet 2 and reed slim, arrives at a downtown restaurant, apologizes for not having shaved and orders a drink. Dressed in a tailored gray suit, small purple chrysanthemum in the lapel, Indian beads peeking through the open neck of a striped shirt, he looks younger than 29.

"I haven't changed since last night," he says.

But the short dark hair, recently shoulder length, is flecked with gray. he wears a small gold earring "I've had it for years"), a trim mustache, and sports a 2-inch long scar above the left eyebrow. "I got that fencing," he says, laughing.

Bill Paley laughs a lot. He doesn't smoke, still bites his nails and pratices yoga. He appreciates fine good, vintage champage and attractive women, not necessarily in that order. "I love women," he grins flirtatiously.

Paley commutes, to Washington from his home in Indian Rocks Beach on the west cost of Florida every few months, and doesn't like the social presures of New York. Washington, he thinks, is looser.

A walking contradiction, Paley drives a classic 1962 Porsche but dosen't own a credit card; wears blue jeans, topped with a rare Indian-embroidered jacket.

In many ways, he is still a product of his parents.

"I was a strange child," he says. "My parents thought I was crazy. I was sent to a psychiatrist when I was 10, got kicked out of schools, started smoking dope when I was 16 and didn't have many friends."

Paley hung around Cambridge in the early '60's - long-haired and bearded pre-hippie days - with the kind of crowd who thought the Fortune 500 was a stock car race.

After a stint in a Swiss boarding school, Paley enrolled in Rollins College. In 1968 he dropped out and was drafted.

"I decided to enlist instead. So I went to Spain for three months, worked on a film called 'A Talent for Loving' as a production assistant, and picked up a very heavy amphetamine habit."

Paley's best friend at the time took him to Morocco for something called "the hash cure." It was lovely," Paley says. "You just stay stoned the whole time."

In 1969, Paley went to Vietnam for 11 months as an Army "combat cinematographer.'

He says he used heroin, regularly, was almost court-martialed for passing out black arm bands in Long Binh on Moratorium Day of that year (an act he describes as more a "symbol of mourning" than to protest the war), and ended up sweeping floors in photo labs.

"Billy's not a killer," says David Kubisch. Paley's best friend and a part owner of The Gandy Dancer.

But Paley says he did carry a non issue 12-gauge shotgun for self-protection, which was not unusual among some non-combat soldiers. "I was going to get of there alive," he says. Back in America, Paley made films for the Armed Forces Information Service and upon his release from the Army spent four months in Piney Point, Md., alone.

"I was a hermit," he remebers. "Nobody knew where I was." Communication with his family was limited. Friends, including Kubisch, came to Piney Point and found Paley. Together they rebuilt an old sailboat, took it to Florida, sold for the boat and bought another. They sailed around the Florida Keys for a few years before Paley came to Washington in 1975.

He had worked at a string of jobs: yacht broker, dolphin trainer, construction worker, photographer, even sold camping lots door-to-door. "I made about 20 bucks at that," he laughs.

Last year Billy Paley met Fred Moore and with Kubisch and one other partner, Lee Mogul, opened The Gandy Dancer. Another restaurant in Baltimore, The Brass Elephant, is set to open this summer, and plans are under way for a third venture, The Biltmore Ballroom on Columbia Road in Adams-Morgan.

"'My son the yacht broker' was a bit sleazy," Bill Paley smiles. "'My son the restauratuer' is a bit better."

For the first time, the self-effacing young man is approaching a degree of success in a business which, ironically, his dynamo father always wanted to pursue.

"I think my father is proud of me," Billy Paley says. "The only thing we could ever relate to together was food."

William S. Paley often traveled to Europe with young Bill in tow, tasting the foreign cuisines and teaching his son to appreciate fine food. Later, when Bill was old enough to travel on his own, he would send his father postcards describing in detail the meals he had enjoyed. His father would, in turn, reimburse Bill for the cost of the meat.

Once last year while Bill was out of town his father showed up at The Gandy Dancer after a black-tie dinner with the Kissingers. Fred Moore, who manages the restaurant, said the elder Paley came through the back entrance, snooped around the kitchen and ordered a bowl of onion soup and an egg-salad sandwich. It was carried out, doggy-bag style, to a waiting black limousine.

"We had a very good time," William S. Paley said in a recent telephone interview in which he gave a rare glimpse at his private life.

"I forget what I had but it was very good. It's a very attractive place. I had a sense that Billy had fallen in with a very good crowd of people.

"You know he's done awfully well," Paley continued. "He's very generous. Very kind. Very lovable. Though he did have a difficult time during his so-called educational experience."

Bounced from private schools to exclusive academies. Bill Paley (in the words of Mark Twain) "never let his schooling interfere with his education."

"I was highly critical of this," Paley's father said. "He wasn't settling down to business. I wanted him to be well-educated."

Victoria Fortune, owner of a P Street antique shop, is a close friend of Billy Paley's and recently spent a week with him in the Bahamas on a yoga retreat. Fortune thinks the restaurant business is good for Paley. He is becoming less shy.

"We play like 10 year olds." Fortune says. "He's childlike, but not childish. There's a big difference." "The Wind in the Willows" is Paley's favorite book.

But Fortune thinks Paley is strong. It would have been easier, she says, for Billy to conform to the Paley life-style.

"But I think he has potential." she says. "And he's very generous."

Fortune remebers the time she found a pile of books on her doorstep, gifts from Paley. As a child he would give away his toys, a practice Paley says "frecked out" his parents.

"He's into warm relationships," Fortune says. "He can't do that in New York because of his family connections. I think he feels funny around those people."

The family connections include half-sisters Amanda Burden, and Hilary Byers, half-brothers Jeffrey and Stanley, and sister Kate. "I'm my father's only son," Bill Paley says quietly.

Stanley Mortimer, "Babe" Paley's son from her first marriage, works for William S. Paley, Inc., handling investments.

"Billy is a free spirit," Mortimer says, "the kind that some people tried to be in the '60's. He's generous and honest, and I don't think he cares much for materialistic things. Billy had different interests."

Bill Paley is currently interested in a number of causes, including the Miccosukee Indians in Florida and NORML, the marijuana lobby, but his No. 1 cause will always be himself. "'I' is my favorite word in the vocabulary," he says with a smile.

William S. Paley denies ever trying to keep his son's name out of print. "You know, friends of mine adore him." he says.

"Was he the bad seed? No, he wasn't bad, just indifferent to a formal education. But he's read a lot. He's a very independent thinker. he does have a very interesting mind. He's different, which is good." The doting father pauses - "And he's a good-looking boy, don't you think?"

Bill Paley is communicating more with his parents these days, and money is still coming through two trust funds. He says he might like to have kids of his own some day, maybe when he's 40. His mother, whose name has remained synonomous with style and elegant living for over 25 years, is seriously ill. His father, the programming genius and television mogul, is 75 years old.

"My family is going through a lot now," young Paley says. "I think I'm more stable than any of them. All my life people have had such great expectations of me. But I love myself. I love my life. I'm a hedonist. I'm having more fun than 99.8 per cent of the world. I'm glad I never chose one career. I get bored so easily, and I never would have had such a great life, met so many great people, done so many great things. Maybe when I'm 40 . . ."