People.com: Ellen Pompeo and her husband, Chris Ivery, are starting a family together, her rep, Jennifer Allen, confirms to PEOPLE.

"It's great news," says Allen. "They're ecstatic."

The Grey's Anatomy star, 39, and Ivery, 41, a music producer, were married by New York City Mayor Michael Bloomberg in a low-key ceremony in November 2007. The couple met in a grocery store in 2003 and began dating six months later.

Pompeo, who's recently been spotted shopping for baby gear around Los Angeles, is not the only Seattle Grace doctor having a baby in real life: Costar Chyler Leigh and her husband, Nathan West, are expecting her third child, a girl, in May.

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