Sauté chopped onion in hot oil in a large Dutch oven over medium-high heat 7 minutes; add garlic, and sauté 2 to 3 minutes.
Stir in chicken pieces, and cook, stirring constantly, until chicken is lightly browned. Stir in 3 cups water and next 5 ingredients; reduce heat, and simmer, stirring often, 10 minutes or until chicken is done.
Place 2 cans of beans in a blender; add broth, and process until smooth, stopping to scrape down sides.
Stir bean pureé, remaining 2 cans of beans, corn, and chiles into chicken mixture in Dutch oven; bring to a boil over medium-high heat. Reduce heat, and simmer, stirring often, 30 minutes or until thoroughly heated. Stir in lime juice just before serving. Garnish, if desired.
Note: Use a handheld submersion blender to pureé the beans and broth, if desired.