Prep the Chicken: If using breasts, slice them horizontally to create thinner cutlets for even cooking.
Pat dry with paper towels.
Make the Marinade: In a bowl, combine olive oil, lemon juice, garlic, oregano, cumin, smoked paprika, salt, and pepper. Stir well.
Marinate: Add chicken to the bowl and toss to coat. Cover and refrigerate for at least 20–30 minutes, or up to 6 hours for deeper flavor.
Prep the Cucumber: Grate the cucumber on the large holes of a box grater.
Squeeze out excess water using a clean kitchen towel or paper towels until mostly dry. This keeps the sauce thick.
Make the Tzatziki: In a bowl, mix Greek yogurt, grated cucumber, olive oil, lemon juice, garlic, dill, salt, and pepper. Taste and adjust salt, lemon, and garlic to your preference.
Chill until serving.
Cook the Chicken: Heat a large skillet or grill over medium-high. Add a light drizzle of oil if needed. Cook chicken 4–6 minutes per side, depending on thickness, until golden and the internal temperature reaches 165°F (74°C).
Rest the Chicken: Transfer to a plate and rest for 5 minutes to keep it juicy.
Slice against the grain.
Serve: Spoon tzatziki over the chicken or serve on the side. Add warm pita, rice, and a simple salad if you like. Finish with a squeeze of lemon and a sprinkle of fresh herbs.