1. Heat a large skillet over medium-high heat. Add chicken to pan. Cook 3 minutes on each side or until browned.
2. While chicken cooks, combine onion and next 9 ingredients (through green chiles) in a 5-quart electric slow cooker. Transfer chicken to slow cooker. Cover and cook on LOW for 4 hours.
3. Remove chicken from slow cooker. Remove meat from bones; discard bones. Return meat to soup. Divide tortilla chips among 8 bowls. Ladle soup over tortilla chips; sprinkle with cheese.