Cut the chicken breasts in half lengthwise. In a bowl, mix lemon juice and zest, garlic, oregano, paprika, salt, and olive oil.
Pour the marinade over the chicken and marinate for at least 3 hours or overnight for best flavor.
Preheat the grill. Prepare toppings by slicing onion, tomato, avocado, and washing lettuce.
Make the feta spread by mashing feta with a fork and mixing with Greek yogurt until combined.
Grill chicken over high heat for 2 minutes per side, then move to indirect heat. Cover and cook for 5–7 minutes until fully cooked (internal temperature 165°F / 74°C).
Rest the chicken for 5 minutes.
Assemble the Greek Chicken Burger with Feta by spreading feta mixture on the bottom bun, adding lettuce, grilled chicken, onion, tomato, and avocado.
Top with tzatziki and the top bun. Serve immediately.