In a bowl, combine olive oil, lemon juice, garlic, oregano, salt, and pepper. Coat the chicken thoroughly and marinate for at least 20 minutes, or up to 2 hours for deeper flavor.
Heat a grill pan over medium heat. Cook chicken for 5 to 7 minutes per side until golden and fully cooked. Internal temperature should reach 165°F (74°C). Let rest before slicing.
In a large bowl, combine cucumber, tomatoes, red onion, olives, and romaine. Add feta cheese on top.
Whisk together olive oil, red wine vinegar, lemon juice, Dijon mustard, oregano, garlic, salt, and pepper until well combined.
Slice grilled chicken and arrange over the vegetables. Drizzle with dressing just before serving. Toss gently or leave layered for presentation.