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Pre-heat grill to medium heat.
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In a small bowl whisk olive oil, vinegar, lime juice, chili powder, paprika, cayenne pepper, minced garlic, salt, and pepper.
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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.
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Alternate one piece of chicken, onion, bell pepper, and zucchini while threading onto skewers. Pour the remaining marinade over the entire skewer.
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Grill for 8 to 10 minutes (about 2 minutes on each side) or until chicken no longer pink.