In a small saucepan whisk the water, peanut butter, sugar, soy sauce, rice vinegar, ginger, sesame oil, cornstarch, sriracha, and garlic cloves until well blended.
Bring to a boil and cook 1 minute, stirring constantly. Set aside.
Cook the noodles in boiling water for 8 minutes (or following package directions).
Combine the noodles, peanut sauce, bok choy, snow peas, carrot, and cooked chicken in a large bowl and toss well to coat.