Warm oil in a skillet over medium-high heat. Sprinkle chicken with salt and pepper, and place skin side down in skillet. Cook 6 minutes, turning once. Transfer to a plate; remove skin. Drain all but 2 Tbsp. fat from pan. Sauté onions and garlic for 5 minutes. Stir onion mixture, chilies, 1 cup water, cumin, chicken, beans and broth into slow cooker.
Cover and cook on low for 6 hours, stirring twice. Remove 1 cup beans plus 1/2 cup liquid from slow cooker. Puree in a blender; return to slow cooker. Shred chicken and return to slow cooker. Serve hot.