Place beans and broth in a slow cooker. Cover and cook on high until beans are tender, 2 hours.
Warm oil in skillet over medium-high heat. Sprinkle chicken with salt and pepper. Place chicken skin side down in skillet; cook until brown, about 4 minutes. Turn and cook for 2 minutes more. Transfer to a plate; remove and discard skin. Drain all but 2 Tbsp. fat from skillet. Add onions and garlic; cook until softened, 5 minutes. Add onion mixture, chilies, 1 cup water and cumin to slow cooker. Stir; add chicken.
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. Remove chicken, shred it and return to slow cooker. Spoon into individual bowls and serve.