In a 5-quart soup pot over high heat, bring broth, onion, carrot, green chilies, garlic, and basil to a simmer. Cover, reduce heat to low, and simmer 15 minutes.
Turn heat to back to high and bring broth to a boil. Add ravioli and cook until just barely tender to bite, 4 to 6 minutes. Add chicken and cook until hot, about 2 minutes more. Ladle soup into bowls, and sprinkle with parmesan cheese.