In a bowl, whisk together olive oil, lemon juice, garlic, oregano, salt, and pepper.
Place chicken in a zip-top bag and pour marinade over it. Seal and refrigerate for 30 minutes to 2 hours.
Preheat grill to medium-high. Grill chicken 5–6 minutes per side or until fully cooked. Let rest, then slice.
In a large bowl, combine lettuce, cucumber, tomatoes, red onion, olives, and feta.
Top with grilled chicken and serve with lemon wedges.