PLACE chicken in medium bowl. Add 1/4 cup of the barbecue sauce and the garlic; toss to coat. Cover and refrigerate at least 20 min. to marinate. Meanwhile, cook spaghetti in large saucepan as directed on package.
MIX dressing, remaining 1 Tbsp. barbecue sauce and the ginger; set aside. Remove chicken from barbecue sauce mixture; discard barbecue sauce mixture. Stir-fry chicken, peppers and carrots in large nonstick skillet on medium heat 5 min. or until chicken is cooked through. Stir in dressing mixture.
DRAIN spaghetti; return to pan. Add chicken mixture and 3 Tbsp. of the cilantro; mix lightly. Sprinkle with remaining 1 Tbsp. cilantro.