In a large skillet, heat olive oil over medium heat. Add the chopped onion and sauté for about 3-4 minutes until softened.
Stir in the minced garlic, oregano, cumin, smoked paprika, salt, and pepper. Cook for an additional minute until fragrant.
Add the ground chicken to the skillet, breaking it apart with a spatula. Cook for 6-8 minutes, or until the chicken is fully cooked and no longer pink.
While the chicken is cooking, prepare the salad by combining the cherry tomatoes, cucumber, olives, and feta cheese in a bowl. Toss gently to mix.
Warm the pita pockets in a toaster or on a skillet for about 1-2 minutes until soft.
To assemble, fill each pita pocket with the cooked ground chicken and top with the salad mixture. Drizzle with tzatziki sauce before serving.