Elizabeth Taylor, star of "Private Lives," apparently isn't afraid to reveal her Public Life. She has asked for a limousine with clear glass windows to replace the one she has with blue, obscure glass. Now everybody can see the star as she glitters to and from the Kennedy Center.

Taylor and Richard Burton, in a switch, are now sending other people candy. Taylor's (obscure glass) limousine stopped at Children's Hospital yesterday to deliver some of the tributes people have been paying her: 12 boxes of Famous Amos chocolate chip cookies, five dozen Vista International Hotel chocolate chip cookies, a gallon of Louis Sherry Famous Amos flavor ice cream and one 8-pound Kron chocolate leg.

The leg, said Daria Ferrentino, Children's Hospital operations manager, "is about as long as mine, 20 inches." It was one of a chorus line that Zev Bufman, producer of "Private Lives," gave to all cast members on opening night Sunday--as in the old theatrical good-luck wish, "Break a leg." Kron Chocolatiers said each leg cost $75. Ferrentino, who seemed more impressed by Taylor's driver than the chocolate, said, "We haven't figured out just what we're going to do with the leg."

Burton, in turn, has surprised the room maids at the Watergate Hotel by sending them a 10-pound box of chocolates.

"Elizabeth Taylor, please call Alvin," read the note on the bulletin board at the posh Dupont Circle exercise club, Diana's, according to owner Diana Hart.

"The notice had hardly been up a minute before pandemonium broke out. All our clients were crowding around the telephone to see Elizabeth Taylor call her parrot," said Hart. "Of course, our Elizabeth Taylor isn't the actress. And her friend is a man, not a parrot."

The exercising Taylor, said Hart, "told me that a lot of things have happened to her because of her name. Some good. Some bad."

Guess who Elizabeth Taylor (the actress, not the exerciser) saw in her hotel lobby as she went out the door to the theater? The new Mrs. Richard Burton (Sally Hay) having a drink with a friend. Taylor and Hay waved.

Private Life for Elizabeth Taylor seems to be one big cast party. Monday night she went to the Copacabana in New York in a Michaele Vollbracht dress for the cast party of "The Corn Is Green," another Elizabeth Theater Group play. Last night, "Private Lives" had a second cast party, this one at The Intrigue Restaurant to welcome Charlotte Moore, who has taken over the "Don't quibble, Sybil" role from Kathryn Walker. (Actress Walker asked to be released from the play because she had a project she "just couldn't resist," said Tiki Davies of the Kennedy Center. Walker, Davies added, said it would need her full concentration for two months.) About 30 from the company came, but that didn't include Burton, who's been going to bed early.

Taylor "eats with us most nights after the production," said Peter La Ricos, who with his wife Barbara owns The Intrigue. "She certainly has been good for business. Our restaurant has quite an after-the-theater business because of her. We've had people try and pay us $50 to $100 for tables where they will be near her. We don't accept, of course. We try and keep people from bothering her.

"We get lots of actors here--Al Pacino playing in "American Buffalo" at the Kennedy Center eats here before the show. Actors tell each other we stay open late. The one we don't get is Richard Burton. One of her (Taylor's) people told me he doesn't come because this is her spot."

Taylor apparently feels at home at The Intrigue. The other night she walked by the phone when it rang--and answered it.