Thaw noodles according to package directions. Meanwhile, melt butter in a large sauce pan over medium-high heat. Add the chopped onion, celery and carrots and saute until the vegetables are just tender, about 5 minutes.

Add chicken broth to vegetables in pot and bring to a simmer. Add chicken breasts and boil until chicken is cooked through, 8-10 minutes.

Remove chicken from pot and shred with two forks; set aside. Add the milk to the pot and return to a boil.

Gently stir the thawed noodles into the broth, along with the shredded chicken.

Cook for about 15 minutes, or until noodles are tender. Stir in cream of chicken soup and simmer a few minutes more.