Pat the chicken dry and slice into thin, even strips for quick, even cooking.
In a bowl, whisk together olive oil, minced garlic, oregano, cumin, paprika, salt, and pepper. Add chicken strips and toss to coat. Let marinate for 5–10 minutes if you have time, or cook immediately.
Heat a large skillet over medium-high heat. Add marinated chicken and cook, stirring occasionally, until fully cooked through and lightly browned, about 6–8 minutes depending on thickness.
Warm the wraps in a dry skillet or microwave for 15–20 seconds to soften them for wrapping.
In a small bowl, stir tzatziki or Greek yogurt sauce with a squeeze of lemon juice and a pinch of salt (optional) to brighten the flavor.
To assemble, lay a wrap flat. Layer greens, cucumber, tomatoes, red onion, and feta. Top with cooked chicken. Drizzle with the yogurt sauce.
Fold the bottom edge up over the filling, then roll tightly from one side to the other. Slice in half and serve immediately.
Optional: serve with a side of lemon wedges for an extra citrusy punch or a quick Greek salad on the side.