Whisk together Greek yogurt, olive oil, lemon juice and zest, garlic, oregano, salt, and pepper in a bowl.
Coat chicken in the marinade and refrigerate for at least 30 minutes (up to 8 hours).
Grill chicken for 5-7 minutes per side, or bake at 400°F (200°C) for 20-25 minutes until internal temperature reaches 165°F (75°C).
Grate the cucumber and squeeze out excess moisture. Mix with Greek yogurt, garlic, lemon juice, olive oil, dill, salt, and pepper to make tzatziki sauce. Refrigerate for at least 15 minutes.
Assemble the salad by combining lettuce, tomatoes, cucumber, red onion, olives, and feta cheese in a bowl.
Slice the grilled or baked chicken and add it to the salad.
Drizzle with tzatziki sauce and toss gently before serving.
Notes
For a heartier meal, serve with warm pita bread, quinoa, or couscous. Store leftovers in an airtight container in the fridge for up to 3 days.