In a medium bowl, combine tuna, cream cheese, water chestnuts, green onions, and parsley.
Blend mayonnaise and chili sauce together in a cup; fold into tuna mixture.
Cut a thin slice from top of each roll; hollow out inside, leaving about 1/2-inch thick shell.
Dividing evenly among the rolls, spoon tuna mixture into shells; set tops of rolls back in place. Wrap each tuna roll in foil; place on a a baking sheet. Bake wrapped tuna buns at 350° for 20 to 25 minutes.
Unwrap tuna buns and serve hot.