Mix the lemon juice, lemon zest, oregano, grated onion, minced garlic, olive oil, salt, and pepper in a bowl.
Pour the marinade over the chicken, then cover and chill for at least 1 hour or overnight.
Once marinated, thread the chicken onto skewers and preheat a grill.
Grill the skewers on medium heat, turning occasionally until cooked through, about 5-7 minutes on each side.