Preheat oven to 350°F. Combine tomatoes with their liquid, 1/2 cup of the cheese, basil and dry stuffing mix; stir just until moistened.
Place 2 chicken breast halves 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 thickness. Repeat process in same bag with remaining chicken breast halves, 2 at a time.
Place chicken, smooth-sides down, on large cutting board. Spread evenly with stuffing mixture. Starting at narrow end, begin rolling chicken, as tightly as possible, around stuffing mixture. Place, seam-sides down, in 13x9-inch baking dish. Drizzle evenly with dressing.
Bake 40 min. Sprinkle with remaining 3/4 cup cheese. Bake an additional 5 min. or until chicken is cooked through (170°F) and cheese is melted.