Drizzle olive oil over the chicken breasts. In a small bowl, combine garlic powder, paprika, oregano, salt, and black pepper. Rub the seasoning mixture evenly over both sides of the chicken.
Heat a large skillet over medium heat. Add the chicken breasts and cook for about 5 to 6 minutes per side until golden brown and fully cooked through. Remove the chicken from the skillet and let it rest for 5 minutes before slicing into thin strips.
While the chicken rests, prepare the vegetables. Chop the romaine lettuce, halve the cherry tomatoes, dice the cucumber, thinly slice the red onion, slice the olives, and crumble the feta cheese.
Warm the tortillas in a dry skillet or microwave for a few seconds until soft and flexible.
Lay each tortilla flat onto a clean surface. Spread tzatziki sauce across the center of each tortilla, leaving space around the edges.
Add lettuce, sliced chicken, tomatoes, cucumber, red onion, olives, and feta cheese evenly onto each tortilla.
Fold the sides inward and tightly roll the tortillas into wraps. Place seam-side down for a minute so they stay closed.
Slice the wraps in half if desired and serve immediately while fresh.