Put the chicken and enchilada sauce into a saucepan. Cover and cook gently, stirring often, until chicken is cooked through, about 15 minutes. Remove the chicken to a bowl and shred. (Keep the enchilada sauce it cooked in.)
Spread some of the enchilada sauce on the bottom of a casserole dish. Cover with 2 tortillas, ⅓ of the shredded chicken, ⅓ of the remaining enchilada sauce and ⅓ of the cheese. Top with 2 more tortillas and repeat layers, ending with cheese. Bake in a preheated 375-degree F oven for about 30 minutes.