In a bowl, combine the ground chicken, chopped dill, diced red onion, oregano, garlic powder, egg, salt, and black pepper. Mix gently until just combined.
Divide the mixture into four equal portions and shape them into burger patties.
Heat a skillet over medium-high heat and add the olive oil.
Place the patties in the skillet and cook for about 3 to 4 minutes on each side until fully cooked and the internal temperature reaches 165°F. Remove the burgers from the skillet and set aside.
While the burgers are cooking, prepare the tzatziki sauce.
Add the cucumber, fresh dill, and garlic to a food processor and pulse until finely chopped.
Transfer the mixture to a bowl with the yogurt and stir until well combined.
Add lemon juice and salt, then mix again. Taste and adjust the salt if needed.
To assemble the Greek Chicken Burgers with Creamy Tzatziki, place a lettuce leaf on a plate, add the cooked chicken burger, and top with tzatziki sauce, sliced tomatoes, and red onion.
Serve immediately.