Heat grill. Cook bacon in medium skillet over medium heat until crisp. Remove bacon from skillet; drain on paper towel. Set aside.
Add vinegar, oil, brown sugar and marjoram to bacon drippings in skillet; cook and stir over medium heat to mix and dissolve sugar. Remove from heat. Reserve about 1/4 cup of vinegar mixture to use as glaze during grilling; set remaining aside for dressing.
When ready to grill, place chicken on gas grill over medium heat or on charcoal grill 4 to 6 inches from medium coals. Cook 5 minutes.
Brush chicken with reserved glaze; turn chicken. Add bell peppers and squash to grill. Brush chicken and vegetables with glaze. Cook about 10 minutes or until chicken is fork-tender and juices run clear and vegetables are crisp-tender, turning chicken and vegetables, and brushing with glaze once or twice. Discard any remaining glaze.
To serve, arrange mixed greens on 4 individual plates. Cut chicken crosswise into slices; place over greens. Arrange bell peppers and squash around chicken. Sprinkle with bacon. Drizzle or serve with reserved dressing.