Pre-heat grill to medium heat.
In a small bowl whisk olive oil, vinegar, lime juice, chili powder, paprika, cayenne pepper, minced garlic, salt, and pepper.
Place chicken pieces in a shallow baking dish. Pour mixture over chicken. Stir to coat chicken well and refrigerate. Allow pieces to marinate at least 30 minutes. For best results, marinate overnight.
Alternate one piece of chicken, onion, bell pepper, and zucchini while threading onto skewers. Pour the remaining marinade over the entire skewer.
Grill for 8 to 10 minutes (about 2 minutes on each side) or until chicken no longer pink.