The clip, released Wednesday, follows Cooper as a successful musician who discovers Gaga and begins to fall in love with her as they work on music together.
"Almost every single person has told me they like the way I sounded but that they didn't like the way I look," Gaga says. Cooper replies, "I think you're beautiful."
Gaga performs original songs in the film which she wrote with Cooper and other artists such as Lukas Nelson, Jason Isbell and Mark Ronson. All of the music in the film is original and was recorded live.
A Star is Born is set to hit theaters on Oct. 5.
"In this new take on the tragic love story, he (Cooper) plays seasoned musician Jackson Maine, who discovers-and falls in love with-struggling artist Ally (Gaga). She has just about given up on her dream to make it big as a singer... until Jack coaxes her into the spotlight. But even as Ally's career takes off, the personal side of their relationship is breaking down, as Jack fights an ongoing battle with his own internal demons," reads the synopsis.