Cook spaghetti as directed on package. Drain.
Meanwhile, heat 1 tablespoon of the oil in wok or 12-inch skillet over medium-high heat until hot. Add chicken; cook and stir 4 to 6 minutes or until chicken is no longer pink in center. Remove chicken from skillet; place on plate and cover to keep warm.
Add remaining tablespoon oil to wok. Add carrot; cook and stir 2 minutes. Add bell pepper and asparagus; cook and stir an additional 2 to 3 minutes or until vegetables are tender.
Add cooked spaghetti and peanut sauce. Return chicken to wok; toss to coat. Cook and stir about 2 minutes or until thoroughly heated.