Season the chicken breasts with olive oil, lemon zest, lemon juice, garlic, oregano, salt, and pepper.
Heat a skillet or grill pan over medium heat. Cook the chicken for 5–6 minutes per side, or until cooked through. Remove from heat and slice.
In a small bowl, mix the Greek yogurt, feta cheese, dill, and lemon juice. Add a splash of water to reach your desired consistency.
Add romaine lettuce to the bowl, then top with cucumber, tomatoes, and red onion. Add sliced chicken and drizzle with the feta yogurt sauce.