In a pot, mix oil, lemon juice, minced garlic, oregano, salt, and pepper.
Add the chicken cubes to the marinade and let sit for 5 minutes (or longer if time allows).
Thread the chicken onto skewers.
Heat a grill pan over medium-high heat. Grill the skewers, turning occasionally, until the chicken is golden brown and cooked through, about 10-12 minutes.
Garnish with chopped parsley and serve with lemon wedges on the side.