1Heat coals or gas grill for direct heat. Place chicken in shallow pan. Drizzle with 1/2 cup of the dressing; turn to coat. Sprinkle with 1/4 teaspoon of the pepper.
2Mix bell peppers, onion, remaining 1/4 cup dressing and remaining 1/4 teaspoon pepper in medium bowl; toss to coat. Place vegetables in grill basket (grill “wok”), using slotted spoon; reserve dressing in bowl.
3Remove chicken from pan; reserve dressing in pan. Place chicken, skin sides up, on grill over medium heat. Cover and grill 40 to 50 minutes, turning occasionally and brushing with dressing remaining in shallow pan, until juice of chicken is no longer pink when centers of thickest pieces are cut. Add grill basket to grill during last 15 minutes of grilling; grill, shaking basket or stirring vegetables occasionally, until vegetables are crisp-tender.
4Add tomatoes, basil and grilled vegetables to bowl with dressing; toss to coat. Serve vegetables with chicken.