In a mixing bowl, combine olive oil, lemon juice, minced garlic, dried oregano, salt, and black pepper to create the marinade.
Add the chicken breasts to the marinade, ensuring they are well-coated. Let them marinate for at least 30 minutes.
Preheat the grill to medium-high heat. Grill the chicken breasts for about 5-7 minutes on each side, or until fully cooked.
Once cooked, let the chicken rest for a few minutes before slicing it into thin strips.
Warm the pita bread on the grill for about 1-2 minutes on each side.
Assemble the sandwiches by placing sliced chicken, lettuce, tomatoes, cucumber, and red onion inside the pita bread.