Heat oven to 375°F. In medium bowl, combine cheese, roasted peppers, olives, shallot, chicken, salt and pepper; mix well.
Unroll dough; place on ungreased cookie sheet. Starting at center, press out dough with hands to form 14x9-inch rectangle. In small bowl, combine egg and water; beat well. Brush lightly over dough.
Spoon cheese mixture lengthwise in 3-inch-wide strip down center of dough to within 1/4 inch of each end. Bring long sides of dough up over cheese until edges touch. Press ends to seal. Brush lightly with egg mixture.
Bake at 375°F. for 20 to 25 minutes or until deep golden brown. Cut into crosswise slices. Serve warm.