In a large skillet, melt the butter over medium-low heat. Add the carrot, celery, and onion. Sautee in the butter until veggies are soft, about 5 minutes. Add the garlic and cook for about 30-60 seconds.

Add the flour and cook for about 3 minutes or until mixture is thick. Slowly whisk in the chicken broth and cream and bring the heat up to medium-high. Add the egg noodles and cook for 5-7 minutes or until noodles are soft.

Add the chicken to the noodles for the last minute or two of cooking to heat the chicken through. Salt and pepper to taste. Serve immediately.