In a bowl, combine the sliced chicken, minced garlic, olive oil, oregano, smoked paprika, salt, and black pepper. Mix until the chicken is well coated. Cover and marinate in the refrigerator for at least 1 hour (or overnight for best flavor).
Preheat a grill or skillet over medium-high heat. Cook the marinated chicken for about 6-8 minutes on each side, or until the chicken is fully cooked and has nice grill marks. Remove from heat and let it rest for a few minutes before slicing it into smaller pieces.
While the chicken is resting, prepare the tzatziki sauce by combining Greek yogurt, lemon juice, diced cucumber, and a pinch of salt in a bowl. Mix well and set aside.
Warm the pitas or flatbreads on the grill or in a dry skillet for about 30 seconds on each side.
To assemble, layer the sliced chicken onto the pitas, top with tomatoes, red onion, and drizzle with tzatziki sauce. If desired, sprinkle crumbled feta cheese over the top.
Garnish with fresh parsley or dill for added flavor and color.
Notes
Marinate the chicken overnight for the best flavor.