Heat gas or charcoal grill. In 12-inch nonstick skillet, cook bacon, stirring occasionally, until crisp; drain on paper towel. Discard all but 2 tablespoons bacon drippings in skillet.
Stir dressing into drippings in skillet. Remove from heat. Remove 1/4 cup dressing mixture from skillet; reserve.
Add carrots, onion, bell peppers and beans to remaining dressing mixture in skillet; stir to coat. With slotted spoon, place vegetables in grill basket (grill "wok"). Reserve dressing mixture in skillet.
Place chicken and grill basket on grill over medium heat. Cover grill; cook 15 to 20 minutes, shaking grill basket occasionally, turning chicken once and brushing reserved dressing mixture from skillet over chicken, until vegetables are crisp-tender and juice of chicken is clear when center of thickest part is cut (170°F).
To serve, arrange vegetables around chicken. Sprinkle with bacon; drizzle with reserved 1/4 cup dressing mixture.