In a bowl, combine olive oil, lemon juice, garlic, oregano, salt, and pepper.
Add chicken cubes to the marinade and mix well.
Cover and refrigerate for at least 1 hour.
Preheat the grill to medium-high heat.
Thread the marinated chicken and vegetables onto skewers.
Place skewers on the grill and cook for 10-15 minutes, turning occasionally.
Ensure chicken is cooked through (internal temperature of 165°F).
Remove from grill and let rest for a few minutes.
Serve with tzatziki sauce and pita bread.
Enjoy your homemade chicken souvlaki!