Sprinkle chicken evenly with Caribbean rub; set aside.
Heat 1 teaspoon oil in a medium skillet over medium-high heat; add onion and garlic. Cook 3 minutes or until tender. Transfer mixture to a 5-quart oval slow cooker using a slotted spoon. Heat remaining 3 teaspoons oil in skillet over medium-high heat; add chicken, and cook 6 to 8 minutes, or until browned, turning occasionally. Transfer chicken to slow cooker. Add 1 cup broth to skillet, scraping skillet to loosen browned bits. Pour over chicken. Add remaining broth, adobo sauce, and next 4 ingredients to slow cooker. Cover and cook on HIGH 1 hour. Decrease temperature to LOW, and cook 3 more hours.
Remove chicken from slow cooker, and cool 10 minutes. Remove chicken from bones, returning meat to slow cooker. Stir in lime juice. Serve soup over hot cooked rice; top with cilantro, radishes, and sour cream. Serve with lime wedges.
* We used adobo sauce from canned chipotle chiles in adobo sauce.