Cook spaghetti according to package directions, omitting salt and adding carrots, pea pods, and sweet pepper for the last 1 minute of cooking. Drain, reserving 2/3 cup of the cooking water. Return pasta mixture to pan. Stir in chicken; cover and keep warm.
In a small saucepan combine peanut butter, soy sauce, rice vinegar, honey, and the reserved cooking water. Cook and stir over medium heat until peanut butter is melted and mixture is smooth.
Pour peanut butter mixture over pasta mixture; toss gently to coat.