'Lost'' s Yunjin Kim

In South Korea, Yunjin Kim is as famous as Julia Roberts, but thanks to ABC’s Lost, Americans are finally getting to know this Pretty Woman. And Kim, who was raised in New York and got her bachelor’s degree at Boston University, is getting a taste of Hollywood-style celebrity. “I come into the airport now and there’s always like 20 people waiting with photographs for me to sign,” she says. While on the Lost set in Hawaii, Kim, 31, who plays the dutiful yet secretive wife Sun, talked with PEOPLE about being single in real life, playing golf – badly – and her surprising wild streak.

You grew up in New York City, but went all the way to Korea to become a star?
Funny, huh? I grew up on Staten Island. I was doing theater in New York. I met this producer who cast me in a Korean miniseries. That miniseries did really well – and it was all in Korean.

I hear you are the Julia Roberts of Korea.
Oh, I don’t know about that, but I like the comparison! (After the miniseries) I did my first feature film, Shiri, in 1999. I played a North Korean spy who falls in love with her enemy. It was very popular all over Asia. (South Korea) was the only country where its own movie beat the record of Titanic.

What was it like coming back to the U.S.?
You have to treat Hollywood like it’s your boyfriend – he’s there all the time. I took mini-trips over and met directors.

Ironic, isn’t it, that you come back to America and you have to keep acting in Korean?
Yes, it is. But you know, the role didn’t exist before I met with J.J. (Abrams, Lost’s creator). He thought it would be interesting to have a Korean couple on the plane, but only after we met. So that’s really flattering.

Your character, Sun, and her husband, Jin, are so serious, but you and actor Daniel Dae Kim are so –
Silly? Yes. We were at this photo shoot one time and I lifted up my skirt and Evie (Evangeline Lilly) was like, “Yunjin, what are you doing? That’s not you!” She just didn’t expect me to do that.

How is island life treating you?

It’s luxurious. I’ve been learning how to golf. Daniel’s wife, Mia, and I took lessons together. I think I need more lessons. I played 18 holes yesterday and it was about my tenth try before I hit the ball! I also bought a condo and I’m spending my days off shopping for furniture.

How has the Asian community reacted to the show?
I know that in Koreatown in L.A., things practically shut down when the show is on because people want to tune in to see these two Koreans go at each other. I heard that people dressed up as Sun and Jin for Halloween last year, too.

What can we expect from Sun in season two?
I don’t think they (the writers) even know. They really do keep the actors in the dark.

So you don’t know who’s next to be killed off?
That’s the hardest thing about doing this show, having that dark cloud floating around all of us. When Boone (Ian Somerhalder) died, that was really hard.

You’re one of the few single cast members on the show. You must get a lot of guys hitting on you.
No! People are very cautious about coming up to you, like you must be very busy or you must have tons of guys surrounding you. I would really like to make it official that it’s not true! Please! God, do I have to make the first move? Maybe.