1. Heat a Dutch oven over medium-high heat. Add oil. Sprinkle chicken with 1/4 teaspoon salt. Add chicken; sauté 4 minutes. Add onion and next 5 ingredients; sauté 3 minutes. Add 2 cups beans, water, 1/2 teaspoon salt, 1 can chiles, and broth; bring to a boil.
2. Mash 1 cup beans and 1 can chiles in a bowl. Add to soup; simmer 5 minutes. Serve with cilantro and lime.