Preheat the oven to 350 degrees F (175 degrees C).
Bring a large pot of lightly salted water to a boil. Add the egg noodles, and cook until tender, about 8 minutes. Drain and transfer to a greased 9x13 inch baking dish.
Melt the margarine in a saucepan over medium heat. Whisk in the flour using a fork so that no lumps form. Gradually stir in the milk. Bring to a simmer, stirring constantly, then add the cheese. Cook and stir until smooth. Stir in the cream of mushroom soup, and then the dried beef. Stir into the noodles in the casserole dish, and top with crushed potato chips.
Bake for 30 minutes in the preheated oven, until the sauce is thick and bubbling, and top is toasted.