Preheat grill to 300° to 350° (medium) heat. Sprinkle chicken with salt and pepper. Combine cheese and next 3 ingredients. Brush chicken with cheese mixture.
Toss zucchini, onion, and bell pepper in olive oil.
Grill chicken and vegetable mixture at the same time, covered with grill lid. Grill chicken 7 to 10 minutes on each side or until done. Grill vegetable mixture 2 to 3 minutes or until crisp-tender. Chop vegetable mixture, and toss with basil. Add salt and pepper to taste. Serve vegetable mixture with grilled chicken.
Originally published on Southern Living, Grilled Chicken and Garden Salsa.