Unroll dough onto a parchment lined baking sheet. Pinch perforations to seal. Place 1/2 of the white BBQ sauce on each 1/3 edge of dough lengthwise, leaving 1/3 of the dough strip down the center. Spoon red sauce on this center strip of dough.
Top with cooked chicken and season with salt and pepper. Top with cheese. Refrigerate for 30 minutes. Roll dough into a log lengthwise, as tightly as possible, pinching any tears and ending with log seam side down on parchment. Refrigerate pan for 30 minutes.
Slice log in half, then slice halves into 6 pieces and lay them cut side up on parchment lined pan.
Bake at 350 for 10-14 minutes or until dough is cooked through and golden. Carefully transfer rolls to serving platter and serve warm with lots of napkins.