Spread cream cheese mixture evenly over entire surface of tortillas. Remove white rib from lettuce leaves. Press lettuce into cream cheese, tearing to fit and leaving top 2 inches of tortillas uncovered. Spread chicken mixture over lettuce. Sprinkle strawberries over chicken.
Firmly roll up tortillas, beginning at bottom. Wrap each roll in plastic wrap. Refrigerate at least 1 hour. Trim ends of each roll. Cut rolls into 1/2- to 3/4-inch slices.