In medium bowl, combine cooked chicken and barbeque sauce. Stir in cheese; set aside. In small bowl, beat egg with water; set aside.
Separate each biscuit into two layers; press each biscuit into a 3-inch circle. Place 1 tablespoon chicken mixture into center of each biscuit; fold biscuit in half over filling. Press edges with fork to seal.
Place on a greased large baking sheet. Brush tops with egg wash. Bake in a preheated 375°F oven 12-15 minutes or until golden brown.