Heat the oil in a large stockpot over a medium flame. Add the garlic, onion, celery and chilies and cook until tender, about 5 minutes.
Stir in all the remaining ingredients, cover and bring to a boil. Reduce heat to simmer and cook until corn and beans are tender and the chicken is heated through, about 8-10 minutes.
Ladle into bowls, top with shredded cheddar and serve with a side of homemade cornbread. (I think this chowder is even better after its sat overnight so I usually make it the day before I intend to serve it.)