In a pan cover chicken breasts with water and salt. Bring to a boil. Lower heat to medium and boil until chicken is no longer pink approximately 20 minutes. Cool and then shred using forks.
Combine cream cheese, soup, sour cream, taco seasoning, and green chilies. I use about 1 1/2 packages of the taco seasoning. You can add more or less depending on how spicy you want the enchiladas. Reserve one cup of sauce for the top of the enchiladas and add chicken to the remaining sauce.
Place three tablespoons of the chicken filling on the edge of the flour tortillas and roll. Place them side by side in a 9×13 pan. Top with reserved sauce and cheese.