In a large soup pot, cook the onion and garlic in olive oil.
Drain one can of beans. Add all three cans of beans to the pot (two with their liquid).
Stir in the chopped green chilis, the seasonings, chicken broth and chicken.
Heat over medium heat until hot through.
Stir milk and cornmeal together and add to the soup.
Adjust salt and pepper.
Heat a few more minutes and serve.