1. Preheat grill to high heat.
2. Cook pasta according to package directions, omitting salt and fat; drain. Place in a large bowl, and keep warm.
3. Place garlic in food processor; process until minced. Add basil and next 4 ingredients (through pepper). With processor on, slowly pour oil through food chute; process until smooth.
4. Brush 1 tablespoon vinegar over onion slices; brush remaining 1 tablespoon vinegar over chicken. Place 2 cups tomatoes in center of each of 2 (24- x 12-inch) pieces of foil. Fold foil over tomatoes; tightly seal edges.
5. Place chicken, onion, and foil pouches on grill rack coated with cooking spray. Grill chicken, onion, and foil pouches 15 minutes or until onion is tender and tomatoes pop, turning all after 5 minutes. Remove onion and foil pouches from grill; turn chicken over, and cook an additional 5 minutes or until done. Let chicken stand 5 minutes. Chop onion; cut chicken into into 1/4-inch slices. Add pesto, tomatoes, chicken, and onion to pasta; toss well. Sprinkle with 1/4 cup cheese; toss gently. Sprinkle remaining cheese evenly over servings. Serve immediately.