In a small bowl combine oil and garlic. Lightly brush tomatoes, then chicken with garlic oil; sprinkle with salt and pepper. Discard any remaining garlic oil.
Prepare grill for indirect heat using a drip pan. Place chicken, bone sides down, over drip pan. Grill, covered, over indirect medium heat 50 to 60 minutes or until done (170 degrees F for breasts; at least 175 degrees F for thighs and drumsticks). Grill tomatoes the last 6 to 8 minutes or until heated through, turning once.
Meanwhile, in a small bowl combine remaining ingredients.
Remove chicken and tomatoes from grill. Immediately spread chicken and cut sides of tomatoes with pesto mixture.