In 2-quart saucepan, mix chicken and 1/2 cup of the enchilada sauce. Heat to boiling over medium-high heat, stirring occasionally.
Separate or cut each can of dough into 4 rectangles (if using crescent rolls, press perforations to seal). Spoon chicken mixture and 1 tablespoon of the cheese onto 1 long side of each rectangle. Roll up; pinch edges to seal. Place seam side down in 13x9-inch (3-quart) glass baking dish. Pour remaining sauce over enchiladas, and sprinkle with remaining cheese.