Abby & Chris Elliott

updated 03/16/2009 AT 01:00 AM EDT

originally published 03/16/2009 AT 01:00 AM EDT

For the last 25 years, Chris Elliott, 48, has been earning laughs by playing lovable losers and silly psychos—from his stints on David Letterman's late-night talk shows and the sitcom Everybody Loves Raymond, to his turns in films like There's Something About Mary and Cabin Boy. Now his oldest daughter Abby, 21, is joining the action. When she started on Saturday Night Live last November, Abby became the show's first-ever second-generation player—thanks to her dad's stint on SNL's 1994-1995 season. But it's not her family ties that are getting her noticed; instead, her gift for hilariously spot-on impressions of stars like Angelina Jolie and Rachel Maddow has earned raves. Father and daughter sat down at the Elliott family home in Old Lyme, Conn., with PEOPLE's Mark Dagostino to talk about growing up funny.

When did you know that Abby had inherited your comedy genes?

CHRIS: I remember taking her to Central Park, and while I was pushing her on the swing, with a completely deadpan face, she'd say, "Who are you? Where's my dad?" I'd have to joke with the moms on either side of me: "Oh, she's a cut-up." You were pretty young when you did that!

ABBY: Like 6 months old.

CHRIS: You couldn't talk yet. You signed it.

When did you realize what your dad did for a living?

ABBY: My first memory of being on a set was [his 1990-1992 TV show] Get A Life. Someone handed me a Ken doll dressed like my dad's character.

CHRIS: Did you think stores had those? It was just a prop!

ABBY: Yeah, but I remember thinking, "I have a Ken doll dressed as my dad." That was different.

Did you always know Abby was destined for showbiz?

CHRIS: In middle school she was in The King and I.

ABBY: Lady Thiang, the King's head wife. Which was very dramatic for 13. (laughs)

CHRIS: She had such a presence, and I remember thinking, "Oh my God. You're going to be a star." But we pushed her. I wanted you to follow in my footsteps. It was all planned before you were born. I just thought you were going to be a boy.

ABBY: And be bald?

CHRIS: What? You still will be, honey. I lost mine at 22. You've got a year.

Abby, did you always want to act?

CHRIS: You wanted to go into medical school.

ABBY: I thought, "I'm gonna drop out of college but go straight into med school."

Did you go to college?

ABBY: I didn't even last a semester. The school part was doable, but the living situation—there were mice crawling up the desk in my dorm room, which was on top of a YMCA.

So you started working with comedy troupes like the Groundlings and Upright Citizens Brigade. How did you land SNL?

ABBY: I just kept sending in tapes. "Look, I can play a yoga instructor and stand on my head!" One character, then four. When they called me to audition, I couldn't speak.

CHRIS: Her audition was great.

ABBY: I did five minutes of impressions: Drew Barrymore, Joan Cusack, Katie Holmes.

CHRIS: She's always been a good mimic. Angelina Jolie I think you started doing when you were 12.

ABBY: When she came out with that whole Gothic thing, with Billy Bob [Thornton]. I started doing her face before the voice: the eyes, the moving.

Have you met Angelina yet?

ABBY: No! I've met Drew, but I haven't done her on the show. And the Olsen twins, who I love to do too.

Did your dad give you any advice?

ABBY: Not a lot of advice, but a lot of support—a lot of letting me know that I can do anything that I want. You couldn't ask for a better family.

CHRIS: Well, you could ask, but you're not going to get it. This is as good as it gets.

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