Heat oven to 400°F. In 10-inch skillet, cook chicken until no longer pink. Transfer chicken to large bowl.
In same skillet, melt butter over medium heat. Stir in flour until well blended. Gradually add chicken broth, beating with whisk after each addition. Make sure mixture is smooth and lump-free before adding more broth. Keep doing this until all of the broth has been added.
Remove skillet from heat. Stir in sour cream with whisk until well combined. Stir in wing sauce. Add cooked chicken; mix well. Set aside.
Unroll dough onto work surface dusted lightly with flour. Cut dough in half; set 1 half aside. Using rolling pin, roll dough until about 1/4 inch thick.
Spoon small amount of chicken mixture into ungreased 11x7- or 12x8-inch (2-quart) glass baking dish. Cut strips of dough to roughly fit on top of chicken mixture; arrange over mixture. Sprinkle some of the cheese over top; add more chicken mixture.
Repeat layering 2 more times, using remaining half of dough and all of the chicken mixture. (Make sure to end with chicken on the surface.) Top with remaining cheese.
Bake 45 minutes or until cheese is golden brown and bubbly. Cool 10 minutes before serving.