Salt and pepper both sides of the chicken breasts. Add oil (I personally prefer to use peanut oil, but olive oil works just fine and doesn't make much of a difference) to large pot and heat on medium. Cook chicken breasts 4-5 min on each side.
While the chicken is cooking take the time to dice the onion and the garlic (or do it before if you prefer). After chicken breasts have cooked remove them and put the onion and garlic in the pot to cook for 5-6 minute.
Cut the chicken breasts into 1/2 inch to 1 inch cubes depending on how big you would like them. The chicken may not be cooked all the way through yet, this is fine and it will finish cooking later.
After the onions and garlic have cooked I like to add the 2 cans of green chilies and cook for a minute. Then add the chicken broth and the cream of mushroom soup (you could use cream of chicken or celery also). Stir well.
Drain and rinse the cans of beans and add those to the pot. Add the cubed chicken as well.
Stir in the cumin and cayenne. When the chili gets to a boil turn the heat down and simmer on low for about 30 minutes.
Salt and pepper to taste and then serve topped with your choice of shredded cheese (the cheddar and Monterey jack is my favorite). Top with sour cream, chopped green onion and/or crackers if you wish.