In a mixing bowl, combine ground chicken, crumbled feta cheese, garlic, parsley, oregano, lemon zest, salt, and pepper. Mix until all ingredients are evenly incorporated.
Divide the mixture into four equal portions and shape each portion into a patty, about 1-inch thick.
Preheat a grill or grill pan over medium-high heat and lightly brush with olive oil to prevent sticking.
Cook the chicken patties on the grill for about 6-7 minutes on each side, or until the internal temperature reaches 165°F (75°C), and the patties are cooked through and golden brown.
While the patties are grilling, prepare the tzatziki sauce by mixing Greek yogurt with additional minced garlic, a pinch of salt, and grated cucumber (squeeze out excess water). Stir until well combined.
Toast the whole wheat burger buns on the grill for about a minute or until lightly browned.
Assemble the burgers by placing a grilled chicken patty on the bottom half of the bun, topped with lettuce, sliced tomatoes, cucumbers, and a generous dollop of tzatziki sauce.
Place the top half of the bun on the burger and serve immediately.
Notes
For extra flavor, let the patties marinate for 30 minutes before grilling.