Combine oil, zest, basil, parsley, scallions, oregano, garlic, salt, and pepper in a large bowl; reserve ¼ cup marinade.
Add chicken to remaining marinade and stir to coat; cover and refrigerate 30 minutes. Meanwhile, alternate threading zucchini and onion onto wood skewers. Brush with reserved ¼ cup marinade.
Heat a grill pan or grill over medium; coat with nonstick spray.
Grill zucchini skewers until vegetables are tender and charred on all sides, 6–8 minutes.
Thread chicken onto 4–6 wood skewers; discard marinade. Grill chicken, covered, until cooked through, turning to grill on all sides, 10 minutes.
