In a bowl, mix together green chilies, 1/4 cup cheese, chicken, and a couple spoonfuls of cream of chicken soup (just enough to hold the mixture together).

Fill tortillas with chicken mixture, roll, and place in a 9x13.

In a small bowl, mix the remaining cream of chicken soup with the milk to create a thick sauce (you can use more or less milk to get the consistency you want).

Pour over rolled enchiladas and top with remaining cheese.

Bake at 350° for 15 minutes.