The Guardians of the Galaxy actor, 39, enjoyed breakfast at the Fairmont Miramar Hotel & Bungalows in Santa Monica, Calif. with his author girlfriend, 28, her famous father and Arnold's girlfriend Heather Milligan on Sunday. This is the first time cameras have spotted Chris meeting his girlfriend's dad since their romance was revealed earlier this year, though he has spent time with her mother, Maria Shriver, and brother, actor Patrick Schwarzenegger.
If this sighting of the family outing is any indication, it seems as though the couple is still going strong. And though they haven't been together very long, a source tells E! News that everyone around them is "rooting" for an engagement.