In a large mixing bowl, combine ground chicken, minced garlic, grated onion, chopped parsley, chopped mint, dried oregano, and crumbled feta cheese. Add breadcrumbs, salt, and black pepper. Mix gently until well combined.

Divide the mixture into four equal portions and shape them into patties, about ¾-inch thick. Rest patties on a plate while preheating the skillet.

Heat olive oil in a skillet over medium heat. Add chicken patties and cook for 5-6 minutes on each side or until they reach an internal temperature of 165°F.

In another bowl, mix Greek yogurt, grated cucumber, minced garlic, lemon juice, and chopped dill. Season with salt and black pepper to make the tzatziki sauce.

Toast burger buns in the same skillet until golden brown, about 2-3 minutes on the cut side.

Spread tzatziki on the bottom of each bun, add lettuce, place the patty, top with tomato slice, and cover with the top bun.