Heat oven to 350°F. Spray large cookie sheet with cooking spray. Unroll dough on cookie sheet; starting at center, press dough into 15x10-inch rectangle. Spread mayonnaise on dough to within 1 inch of edges.
In 10-inch skillet, heat oil over medium-high heat. Cook carrots and celery in oil, stirring frequently, about 5 minutes or until vegetables begin to soften. Stir in salt and pepper. Spread mixture on dough. Top vegetable mixture with chicken. Starting at 15-inch side, roll dough tightly. Pinch edges of dough to seal; turn ends under. Arrange roll diagonally on cookie sheet, seam side down.
Bake 30 to 35 minutes or until golden brown. Cool 5 minutes. Cut into 12 slices.