Heat oil in a large nonstick skillet over medium-high heat. Place peppers, onion, garlic, 1 tablespoon cumin and 1 teaspoon coriander in skillet; cover. Cook, stirring, for 6 minutes.
Transfer vegetables to slow cooker; add chicken, beans and broth. Cover; cook on HIGH for 4 hours or on LOW for 6 hours.
Remove chicken with a slotted spoon. Check liquid for bones. Stir in remaining 1/2 teaspoon each cumin and coriander, lime juice and salt.
Shred chicken meat; stir into slow cooker. Serve with sour cream and cilantro, if desired.
