Prepare noodles according to package directions. Drain and cool. Combine noodles, chicken, and next 4 ingredients (through water chestnuts) in a large bowl; toss well.
Combine chili sauce and next 5 ingredients (through ginger) in a small bowl, stirring with a whisk. Drizzle chili sauce mixture over noodle mixture; toss gently to coat. Sprinkle with peanuts. Serve immediately.