Stir together first 5 ingredients. Place 1 cheese slice on each of 6 bread slices; spread evenly with chicken mixture, and top with remaining cheese and bread slices. Spread half of butter evenly on 1 side of each sandwich.
Cook sandwiches, buttered side down, in a nonstick skillet or griddle over medium heat about 3 minutes or until lightly browned. Spread remaining butter evenly on ungrilled sides; turn and cook 3 minutes or until lightly browned.