Whisk the olive oil, lemon juice, garlic, oregano, salt, and pepper into a marinade.
Add the chicken chunks, toss to coat, and marinate for at least 1 hour.
Soak wooden skewers in water for 20 minutes, then thread on the chicken.
Preheat a grill or grill pan to medium-high.
Grill the skewers for 10-12 minutes, turning, until charred and cooked through.
Rest a few minutes, then serve with lemon wedges.