Set aside 1 seasoning packet from the ramen noodles to use in the recipe; toss the other one.
In a large saucepan bring 2 quarts water to boiling. Break up the noodles slightly and add to the water along with the cut-up vegetables. Return to boiling; reduce heat. Boil gently, uncovered, for 3 minutes. Drain and return to the saucepan.
Meanwhile, for the sauce, in a medium saucepan whisk together the 1¼ cups water (or coconut milk), peanut butter, soy sauce, brown sugar, cornstarch, crushed red pepper, and the seasoning packet. Whisk until smooth. Cook and stir over medium heat until thickened and bubbly. Cook and stir for 2 minutes more. Add the chicken, water chestnuts, and bamboo shoots to the sauce; heat through.
Add the chicken mixture to the noodle mixture in the large saucepan. Toss to combine. Top with peanuts and green onions. Serve!