In a medium bowl, whisk together the olive oil, lemon zest, garlic, parsley, salt, and pepper.
Add the chicken pieces to the bowl and mix to coat with the marinade.
Cover and refrigerate for at least 2 hours and up to 8 hours.
Prepare a medium fire grill.
If using wooden skewers, soak them in water for at least 20 minutes before use.
Thread the chicken pieces onto the skewers and discard the excess marinade.
Lightly oil the grill grates.
Place the kabobs on the grill, cover, and cook until chicken is opaque throughout, about 8-12 minutes, turning over once or twice during cooking.
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