Place 2 of the chicken breasts in large freezer-weight resealable plastic bag. Pound chicken with the side of a heavy can, rolling pin or meat mallet until chicken is 1/4-inch thick. Remove chicken from bag; set aside. Repeat with remaining 6 chicken breasts, two at a time. Place chicken, top-sides down, on large cutting board. Place 1 ham slice on each breast; top with 1 cheese piece. Spread evenly with stuffing mixture. Starting at one of the short ends, tightly roll up each chicken breast. Place, seam-sides down, in 13x9-inch baking dish. Drizzle evenly with dressing.