WHEN SHE WAS BORN ON Aug. 27 in South Miami Hospital, Sophia Rose Stallone seemed picture-perfect. While her mother, model Jennifer Flavin, 28, sat back blissfully in her hospital bed, the baby's father, Sylvester Stallone, 50, couldn't contain his jubilation over their 7 lb., 4 oz. daughter. "It was so incredible watching my father hold that baby," says Stallone's son Sage, 20. "I don't think I've ever seen him look that happy." Adds Flavin's mother, Shirley, 60: "Sly couldn't keep his hands off her."

About a month later, joy turned to alarm when Flavin took Sophia to her Miami pediatrician for a checkup. Dr. Jose Wenger saw the baby wasn't gaining weight and listened to her chest. "I could hear a heart murmur," he says. Wenger suspected a ventricular septal defect—a tiny hole left when the chambers of the heart do not grow together uniformly—that an Oct. 29 echocardiogram at UCLA Medical Center in L.A. confirmed. Soon afterward the couple issued a statement: "We are concerned but optimistic about the outcome."

They should be. The condition isn't life-threatening—two in 1,000 newborns have it—and 70 percent recover without surgery. But Stallone has suffered parental pain before. In 1982, Seargeoh, then 3 and the younger of his two boys with first wife Sasha Czack, was diagnosed with autism. Now the couple hopes Sophia, who has been prescribed daily heart medication along with a diuretic to control congestion in her lungs, will recover on her own. Even if she needs surgery, Wenger says, "we don't expect problems." As grandma Flavin sees it, "Sophia is beautiful, responsive and bright. Everything will be fine."