Preheat your oven to 400°F (200°C). Place the naan breads on a baking sheet.
In a medium bowl, combine the Greek yogurt, minced garlic, dill, lemon juice, olive oil, salt, and pepper. Mix well to create the tzatziki sauce.
Spread half of the tzatziki sauce evenly over each naan bread.
Top the naan with shredded chicken, diced cucumber, and halved cherry tomatoes.
Sprinkle crumbled feta cheese over the top of each naan.
Bake in the preheated oven for 10-12 minutes, or until the naan is crispy and the cheese is slightly melted.
Remove from the oven and drizzle with any remaining tzatziki sauce. Garnish with fresh parsley before serving.