Melt butter in a large pot over medium-high heat. Add onion and celery and sauté for 5 minutes. Add garlic and cook an additional minute, stirring continuously.
Sprinkle flour on top and cook for 2-3 minutes or until flour turns golden brown.
Mix in green chiles and chicken broth then bring to a boil. Once boiling, reduce heat to medium-low and let simmer for 10 minutes.
Add corn, salt, pepper, milk, cooked chicken and cheese. Cook for 10 minutes, or until corn and chicken are heated through and cheese is melted.