Prepare noodles according to package directions, drain, and set aside. Preheat oven to 350 degrees F.
Drizzle avocado slices with lime juice and set aside. Melt butter in a 2-quart saucepan over low heat. Stir in flour, salt, and Tabasco over low heat until mixture bubbles.
Add half-and-half slowly, stirring constantly until mixture thickens.
Add cheese and stir until it has melted. Reserve 1 cup of this sauce. Mix remainder with cooked noodles. Place chicken in bottom of a 9-by-l2-by-3-inch rectangular baking dish. Cover with chopped green chiles.
Spoon noodle mixture over chicken and chiles. Place avocado slices on top and pour reserved sauce over avocados. Bake, uncovered, 35 minutes.