Heat the oil in a Dutch oven or large pot. Dice the chicken into one-inch cubes and sauté them in the hot oil until they are golden brown. Add the diced onions and cook until they are softened.
Add butter and flour. Sauté and mix until no lumps of flour remain.
Add the beans, corn, spices, chicken stock base, and 12 cups of hot water. Let the soup simmer for about 30 minutes.
Pour in the milk and cook the soup for an additional 10 minutes.
Season the chili to taste with salt and pepper, and serve it while it's hot. Top it with shredded cheddar cheese, tortilla chips, and a squeeze of lime juice.