Mix barbecue sauce, vinegar, Worcestershire sauce and soy sauce.
Pour over chicken in resealable plastic bag; seal bag. Refrigerate 2 hours to marinate.
Remove chicken from marinade; discard bag and marinade. Cook chicken in smoker with a combination of apple, hickory and oak woods at 225F for 30 to 45 min. or until chicken is cooked through (165F).
Remove chicken from smoker; cover.
Let stand 15 min.
Meanwhile, cook pasta as directed on package and heat sauce in large saucepan as directed on package. Stir asparagus, peppers and basil into sauce.
Add pasta; toss to coat.
Place pasta mixture on serving platter.
Cut chicken into thin slices; place on top of pasta. Arrange asparagus tips around chicken; sprinkle with Parmesan cheese.