PREHEAT barbecue to medium heat. Brush chicken with oil. Grill chicken 6 to 8 min. on each side or until cooked through (170ºF). Remove from barbecue; let stand 5 min. before cutting into strips. Place in medium bowl.
ADD cheese, tomatoes, dressing and chili powder; toss to coat. Spoon evenly down centres of tortillas. Fold in opposite sides of each tortilla; roll up burrito-style.
GRILL wraps, seam-sides down, 8 to 9 min. or until golden brown, turning after 5 min.