Heat oven to 375°F. Spray 13x9-inch (3-quart) glass baking dish with cooking spray. In large bowl, mix beans, tomatoes, chicken, vinegar and salt.
Unroll dough; separate into 12 breadsticks. Cut each breadstick into 4 equal pieces. Stir 1/4 of breadstick pieces at a time into bean mixture. Stir in 1 cup of the cheese. Spoon into baking dish, gently smoothing top. Top evenly with remaining 1 cup cheese; sprinkle with basil.
Bake 25 to 30 minutes or until bubbly and top is golden brown. To serve, spoon into individual shallow soup bowls; sprinkle with parsley.