Cut the chicken into even bite-sized cubes.
In a bowl, whisk together olive oil, lemon juice, garlic, oregano, red wine vinegar, salt, and black pepper.
Add the chicken to the marinade and coat well.
Cover and marinate in the refrigerator for 30 minutes to 4 hours.
If using wooden skewers, soak them in water for 20 to 30 minutes.
Thread the marinated chicken onto skewers.
Preheat a grill or grill pan over medium-high heat.
Cook the skewers for 10 to 12 minutes, turning occasionally, until the chicken is lightly charred and cooked through.
Let the chicken rest for a few minutes.
Serve with pita bread, tzatziki, red onion, cucumber, and tomato.