Add olive oil, lemon juice, white wine vinegar, minced garlic, dried oregano, salt and pepper to a small mixing bowl or measuring cup; whisk until well incorporated.
Place chunks of chicken in a bowl and pour marinade over them. Mix to coat really well, cover and place in the refrigerator to marinate for a couple of hours, or better yet, overnight.
Place skewers to soak in cold water for about 30 minutes before you start building your kebabs.
Preheat outdoor grill (or grill pan) to medium-high heat.
Remove chicken from the marinade and skewer onto bamboo sticks. Discard unused marinade.
Grill the kebabs, turning them a few times, until chicken is cooked through, is nicely browned and has nice grill marks and is no longer pink in the center, about 10-12 minutes total.