The “You’re So Vain” singer on good friends, lasting love and her greatest fear.

I HAD A PRIVILEGED CHILDHOOD

Growing up in New York City the daughter of Richard Simon, a co-founder of the publishing company Simon & Schuster, and Andrea Heinemann, a civil rights activist, Carly and her siblings were exposed to artists and intellectuals from early on. “It was like a gift to have their friends around,” says Carly, 80. “Oscar Hammerstein and Richard Rodgers and Max Eastman.”

I STARTED OUT SINGING WITH MY SISTER

“I kept asking her to teach me the guitar. Lucy was my guitar mentor,” recalls Carly of her older sister, with whom she made three albums in the 1960s. “Eventually, we both got guitars, and then it was no-holds-barred.”

I HAVE STAGE FRIGHT

“I think the whole experience of being in front of people, exposing yourself and your talent is so unnatural,” says Carly, who once collapsed before a show due to extreme anxiety. “The paradox of it all is I absolutely love to perform.

JOHN TRAVOLTA IS A GOOD FRIEND

The onetime NYC neighbors have been close since the 1970s — and even dated briefly! “He was more wonderful to me than any of them,” she says, comparing the Grease actor to other former loves. In 1997, the two recorded a duet, “Two Sleepy People,” on Carly’s album Film Noir.

I STILL LOVE MY EX

They haven’t spoken since their 1983 divorce, but Carly admits she still has feelings for singer James Taylor. “I will never love anyone again so much or in the same way,” she says.