Add the chicken & the marinade ingredients to a small container with a lid or a ziplog bag; massage the ingredients together & leave to rest in the refrigerator for a few hours or overnight.
When ready to cook, preheat the grill to 325F.
Cook the chicken for 8 minutes on each side (6 minutes for breast) or until the internal temperature of the chicken reaches 165°F, brushing with the marinade once during cooking.
Remove the chicken; cover & allow to rest while you prepare the Tzatziki yogurt sauce
Slice the chicken and lay onto the wraps, spoon the yogurt sauce over the top