Jessica Alba and husband Cash Warren have welcomed a baby girl.

Honor Marie Warren was born June 7 in Los Angeles, her rep, Brad Cafarelli, confirms. This is the couple’s first child.

Alba, 27, and Warren, 31, quietly wed on May 19 at the Beverly Hills courthouse. The two met while working on Fantastic Four, for which Warren was the director’s assistant. They became engaged last December.

The actress recently did some last-minute shopping for baby gear at Bel Bambini on Robertson Boulevard in Los Angeles, picking up items such as Born Free baby bottles and a Boppy pillow for breastfeeding.

“She seemed relaxed,” says a source, “and ready to welcome home her baby.”

As for the kind of parent she plans to be, the actress recently told Fit Pregnancy that she’ll walk the line between tough and nurturing. “I don’t want to be my child’s best friend. I want to be a mom,” she said. “But I do want my child to come to me when they have problems and need to talk, so it’s going to be about treading that line.”