In a medium bowl, combine shredded chicken with olive oil, lemon juice, oregano, and salt and pepper to taste. Mix well and let it sit for 5 minutes.

Lay out whole-wheat wraps on a clean surface or plate. Spread a generous layer of Greek yogurt over each wrap.

Distribute diced cucumbers, halved cherry tomatoes, sliced red onions, and crumbled feta cheese over the wraps.

Spoon the marinated chicken mixture in a straight line down the center of each wrap.

Roll the wrap tightly from one edge while tucking in the sides, then place seam side down on a cutting board.

Slice each wrap diagonally in half and serve immediately.