Cook the spaghetti according to package directions; drain well.
Meanwhile, in a large saucepan, combine cooked chicken, cream of mushroom soup, and milk. Cook, stirring frequently, over medium heat until chicken is heated through and sauce is hot.
Stir in 2/3 cup shredded Parmesan cheese.
Add drained spaghetti to saucepan, and toss gently to coat pasta with sauce. If desired, garnish with additional Parmesan cheese.