In 3- to 4-quart slow cooker, mix chicken, rice, salsa, broth and chiles.
Cover; cook on Low setting 6 to 7 hours.
About 5 minutes before serving, turn off heat on slow cooker. Stir in sour cream and half of the cheese; sprinkle remaining cheese over top. Cover; let stand 5 minutes or until cheese is melted. Serve with additional salsa if desired.