Marinate the chicken by combining olive oil, minced garlic, dried oregano, lemon juice, salt, and pepper in a bowl. Cover and refrigerate for at least 30 minutes.

Cook the marinated chicken in a skillet over medium heat for about 8 minutes until golden brown and cooked through.

Prepare the tzatziki sauce by mixing grated cucumber, Greek yogurt, minced garlic, lemon juice, salt, and pepper in a bowl.

Slice the cherry tomatoes and red onion for assembly.

Warm the tortilla wraps in a skillet or oven to make them pliable.

Assemble the wraps by layering cooked chicken, tzatziki sauce, tomatoes, onions, and feta in each tortilla.

Wrap and slice the tortillas, garnishing with fresh parsley before serving.