Cut the chicken breasts into 1-inch cubes and set aside.
In a mixing bowl, combine the olive oil, lemon juice, minced garlic, dried oregano, salt, and black pepper. Whisk until well blended.
Add the chicken cubes into the marinade, ensuring they are well coated. Cover the bowl and refrigerate for at least 30 minutes (up to 2 hours for more flavor).
If using wooden skewers, soak them in water for about 30 minutes to prevent burning. Preheat the grill or grill pan over medium-high heat.
Thread the marinated chicken cubes onto the skewers, leaving a little space between each piece for even cooking.
Brush the grill with a little olive oil to prevent sticking, then place the skewers on the grill.
Grill the chicken for about 10-15 minutes, turning occasionally, until fully cooked and no longer pink inside. The internal temperature should reach 165°F (75°C).
Remove the skewers from the grill and let them rest for a couple of minutes before serving.
Serve the Chicken Souvlaki with warm pita bread, tzatziki sauce, and fresh vegetables.