In a bowl, whisk together the olive oil, 2.5 tbsp lemon juice, minced garlic, oregano, paprika, salt, pepper, and red pepper flakes until well combined. Add the chicken chunks and toss to coat evenly, ensuring all pieces are well covered with the marinade. Let the chicken marinate for at least 15 minutes, or up to 45 minutes if time allows—the longer it sits, the more flavorful it becomes. I find that even 20 minutes makes a noticeable difference in the depth of flavor.
While the chicken marinates, prepare the fresh salsa. In a bowl, combine the diced cucumbers, seeded and diced tomatoes, diced bell pepper, finely chopped red onion, and fresh parsley. Add the crumbled feta cheese and toss gently to combine. Dress the salsa with 1 tbsp lemon juice, a pinch of salt, and a crack of pepper to taste. I like to let this sit for a few minutes so the flavors meld together—it tastes so much better than if you assemble it right before serving.
Heat a large skillet over medium-high heat until it's hot and shimmering. Working carefully, transfer the marinated chicken from the bowl to the hot skillet in a single layer, letting any excess marinade drip back into the bowl—don't crowd the pan, as the chicken needs space to develop a golden crust. Cook for 3 to 5 minutes without moving the pieces, then flip each chunk and cook for another 3 to 4 minutes until the chicken is golden brown on the outside and cooked through. The internal temperature should reach 165°F when checked with a meat thermometer.
While the chicken finishes cooking, warm the pitas. You can do this directly over a gas flame, in a dry skillet for about 30 seconds per side, or wrapped in foil in a 350°F oven for 5 minutes—this makes them pliable and easier to fill without tearing. Once the chicken is cooked through and the pitas are warm, arrange them on a serving platter. Fill each pita with a generous portion of the seared chicken, top with a spoonful of the Mediterranean salsa from Step 2, and drizzle with tzatziki for creaminess and cooling contrast.