Combine chicken and ½ cup dressing in a 1-gallon recloseable food storage bag; seal. Toss to coat; marinate, refrigerated, 30 minutes or up to overnight.
Prepare grill to medium heat. Remove chicken from marinade; discard marinade. Place chicken on grill; grill 10-12 minutes or until internal temperature reaches 170°F, turning once. Remove from grill and let stand 5 minutes; chop.
Meanwhile, prepare pasta according to package directions. Rinse with cold water; drain. In blender, combine remaining dressing, basil leaves, lemon zest and lemon juice; purée. Salt and pepper to taste.
In large mixing bowl, combine pasta, chicken, cheese, tomatoes and basil dressing; toss to coat. Cover and refrigerate several hours or up to overnight. Toss with pine nuts just before serving.