In a large bowl, combine the shredded lemon peel, lemon juice, chopped parsley, olive oil, minced garlic, salt, and black pepper; whisk until emulsified.
Add the bite-sized chicken pieces to the bowl and toss thoroughly to coat with the marinade; let the chicken marinate for 30 minutes.
Thread the marinated chicken pieces and grape tomatoes onto metal skewers, alternating pieces as desired.
Preheat an outdoor grill to medium heat. Place the skewers on the grill and baste occasionally with any remaining marinade.
Grill the skewers until the chicken is cooked through and slightly charred on both sides, about 3–4 minutes per side depending on heat and piece size.
Remove skewers from the grill and serve immediately.