In a 4-quart Dutch oven, cook spaghetti according to package directions, adding vegetables for the last 2 minutes of cooking time; drain.
For peanut sauce, in a small saucepan, combine peanut butter, sugar, soy sauce, water, vegetable oil, garlic, and crushed red pepper. Heat until peanut butter is melted and sugar is dissolved, stirring frequently.
In a large bowl, combine pasta mixture, peanut sauce, and shredded chicken. Toss well to coat. Serve immediately. If desired, top with chopped peanuts and/or sliced green onion.