Add all of the ingredients for the chicken to a gallon sized zippered bag. Mix everything together and let marinate, at least 30 minutes (up to overnight).
Preheat oven to 375degF.
On a baking rack over parchment paper covered baking sheet, add pieces of chicken. Place in oven for 20 minutes. Remove to a bowl to cool slightly. Then chop or shred into small pieces.
In a sauce pan over medium high heat, add butter, garlic and onion powders. Once melted whisk in the flour and let cook for 2 minutes. Add in seasonings and then whisk in milk slowly, allowing it to thicken. Let cook for 2 minutes then add green chilies. Add the cheese in by the handful and continue to whisk until combined.
In a 13x9 baking dish, add a thin layer of cheese sauce in the bottom. Fill each tortilla with a portion of chicken and then a tablespoon cheese sauce. Roll up top to bottom and place in baking dish.
Pour remaining cheese sauce over top of filled tortillas. Sprinkle shredded cheese evenly over top. Place in oven for 15 minutes. Let sit for 5 minutes before serving.