Bring broth to a simmer in a medium saucepan (do not boil). Keep warm.
Heat oil in a medium sauté pan over medium heat. Add onion and pepper; sauté 5 minutes. Add oats; cook 2 minutes, stirring constantly. Stir in wine; cook 2 minutes or until nearly absorbed, stirring constantly. Add broth, 1/2 cup at a time, stirring until each portion of broth is absorbed before adding the next (about 20 minutes). Stir in chicken, cheese, rosemary, and salt.