AS 8-YEAR-OLDS, JILL HENNESSY AND her identical twin, Jacqueline, often retreated to the basement chez Hennessy to act out scenes from Grease—and treat themselves to spirited sibling rivalry. "We fought over the John Travolta part," says Jill, "because nobody wanted to be Olivia Newton-John. She was the nice one."

These days playing nice is paying off for Hennessy, 26, now in her third season as Claire Kincaid, the sexy, savvy assistant D.A. on NBC's six-year-old Law & Order. Though the show has been something of a revolving door for its stars—Chris Noth, sole survivor of the original cast, was replaced this season by Benjamin Bratt—Hennessy's job seems secure. The willowy 5'8" actress shrugs off all the turmoil. "There wasn't as much as the first year," says Hennessy. "In this business, the rug can get pulled out from under your feet anytime."

Hennessy's security certainly has something to do with her onscreen chemistry with boss Jack McCoy (Sam Waterston, who joined the cast last season). There's sexual tension, but no sex—yet. "That would be like showing Notorious and having Cary Grant and Ingrid Bergman kiss in the first scene," says Hennessy. Adds Waterston, 55: "Jill calls it the 'Where's Waldo?' relationship. It's there, but it's hard to find."

Feeling settled is a new experience for Hennessy. Her father, John, a sales and marketing executive, moved the twins (still known, inevitably, as Jacq and Jill), kid brother John Paul, now 21, and their mother, Maxine, all over Canada, relocating nine times in 12 years. "Each time, I remember just crying and saying, 'Why do we have to leave?' " recalls Jill, who was born in Edmonton, Alta. Adds Jacq: "We always depended on each other as best friends were left behind." Their parents split in 1982, and the children lived with John, mainly in Kitchener-Waterloo, Ont. (Maxine is now a secretary in Montreal.) The trauma of their parents' split was eased somewhat by their paternal grandmother, Eleanor, 77, who, says Jill, "saw a difficult situation and was so supportive of us." She drove Jill, then 15, to modeling school in Toronto, and Hennessy became a model for the money,/ though acting was always her true passion. "[Modeling] deepened any insecurities I already had about how I looked," she says.

At 18, after opting out of the usual 13th preparatory year for college in Ontario, Hennessy headed for Toronto to launch her acting career. "I thought if I didn't try it then, I'd regret it for the rest of my life," she says. But stardom eluded her—as did nice-girl roles. She specialized in playing vampires and prostitutes in TV series such as The Hitchhiker and Friday the 13th, and the 1988 thriller Dead Ringers, with Jeremy Irons, in which Jacq and Jill were cast as twin hookers. Jacq graduated from the University of Waterloo, while still doing commercial work in the summers, and is now a grad student in French literature at the University of Manitoba. Jill stuck with acting. In 1993 she impressed Law & Order co-executive producer Dick Wolf with "her obvious intelligence and a real undercurrent of sex appeal."

Her prime-time presence established, Hennessy now has her eye on the big screen. She's starting small, playing a reporter in a drama titled I Shot Andy Warhol, due early next year. The actress also recently hit the catwalks at the New York City fashion shows, joining other hot young stars like Circle of Friends' Minnie Driver. "The free Nicole Miller dress sealed the deal," jokes Hennessy.

After grueling days maintaining Law and Order, which is filmed in New York City, Hennessy likes to hang out with nonceleb friends in coffee bars near her Upper West Side apartment. Other nights, she straps on a guitar and joins pals Andy Gods-berg and Wally Nichols onstage for a couple of songs in their alternative-folk band the New Originals. But her heart belongs to lawyer-actor Paolo Mastropietro, a wild-maned Antonio Banderas look-alike. She also spends a lot of time with Jacq. Last Christmas the twins traveled to Italy together, where, Jill says dreamily, they "geared our days toward the next meal and sang some songs in French and Spanish for some aristocrat who owned the house we were staying in."

So with a dashing beau and a hit series, what more could Hennessy ask for? Plenty. "I'd like to be the third Indigo Girl," she says, referring to the folk-rock duo. "That and doing a spot on The Simpsons, and I'd be set!"

ANDREW ABRAHAMS in New York City