Preheat your oven to 400°F (200°C).
Place the naan breads on a baking sheet and brush each with olive oil.
Spread 1/4 cup of tzatziki sauce on each naan, leaving a small border around the edges.
Evenly distribute the shredded chicken over the tzatziki sauce on each naan.
Top with diced cucumber, cherry tomatoes, and red onion.
Sprinkle shredded mozzarella cheese over the top of each naan.
Season with dried oregano, salt, and pepper to taste.
Bake in the preheated oven for 10-12 minutes, or until the cheese is melted and bubbly.
Remove from the oven and let cool for a few minutes. Garnish with fresh parsley if desired.
Slice and serve warm.