Aaron Sorkin and Kristin Davis step out together

(CBS News) Screenwriter Aaron Sorkin and actress Kristin Davis stepped out on the red carpet together Wednesday night in Los Angeles.

Romance speculation has been brewing for months, and apparently they aren't hiding it anymore.

Sorkin and the "Sex and the City" star were snapped kissing at the premiere for Sorkin's new HBO series, "The Newsroom."

Sorkin, 51, was married to entertainment lawyer Julia Bingham from 1996 to 2005. They have a 12-year-old daughter together.

Davis, 47, has never been married. In the past, she's been romantically linked to Steve Martin and Alec Baldwin. She adopted a baby girl, Gemma, in 2011.