Marinate the Chicken : In a bowl, combine olive oil, lemon juice, minced garlic, oregano, paprika, salt, and pepper. Add chicken, coat evenly, and marinate for 30 minutes to 2 hours in the refrigerator.
Prepare Tzatziki Sauce : Grate cucumber and squeeze out excess moisture. In a small bowl, combine Greek yogurt, cucumber, minced garlic, olive oil, lemon juice, dill, salt, and pepper. Mix well and refrigerate until serving.
Cook the Chicken : Preheat a grill, grill pan, or skillet over medium-high heat. Cook chicken 5–7 minutes per side until fully cooked (internal temperature 165°F / 75°C). Let rest for 5 minutes, then slice thinly.
Prepare Vegetables and Pita : Chop romaine lettuce, slice tomato, and thinly slice red onion. Warm pita bread on a skillet or in the oven for a few minutes.
Assemble the Wraps : Place lettuce on the pita, add tomato and onion slices. Layer with sliced chicken, then spoon a generous amount of tzatziki sauce on top. Optionally sprinkle with feta cheese and olives.
Fold and Serve : Fold pita over the filling, securing with parchment paper or toothpicks if needed. Serve immediately while warm and fresh.