In a large mixing bowl, combine the ground chicken, breadcrumbs, grated Parmesan, finely chopped onion, minced garlic, dried oregano, dried thyme, salt, black pepper, and chopped fresh parsley. Mix until just combined.
Form the mixture into small, golf-ball-sized meatballs, about 1 to 1.25 inches in diameter.
Heat olive oil in a large skillet over medium heat. Add the meatballs in a single layer and cook for about 4-5 minutes per side until browned and cooked through (internal temperature 165°F).
While meatballs cook, slice cucumbers and halve cherry tomatoes. Stir store-bought tzatziki or keep homemade chilled.
Warm the pita pockets in a dry skillet or microwave until soft and pliable.
Open each pita pocket, spread about 2 tablespoons of tzatziki inside, add 4-5 meatballs, then top with cucumbers, cherry tomatoes, and crumbled feta. Serve immediately.
