Heat a large skillet over medium-high heat. Place chicken breast into skillet and cook and stir until no longer pink in the center, about 10 minutes. Divide chicken, 1 1/2 cups Cheddar cheese, and onions evenly among the tortillas then roll up each tortilla and place seam side down in a 9x13 inch baking pan.
Heat the cream of chicken soup and green chiles in a saucepan over medium heat. Stir in sour cream. Continue stirring until heated though, about 10 min. Pour sauce over tortillas and sprinkle remaining Cheddar cheese on top. Bake in the preheated oven until sauce is bubbling and the Cheddar cheese is melted, about 25 minutes.