Place one sheet phyllo dough on a work surface; brush with melted butter. Repeat with 2 more sheets or phyllo, brushing each layer. (Keep remaining phyllo dough covered with plastic wrap and a damp towel to prevent it from drying out.)
Season chicken with lemon-pepper. Place 1 chicken breast along one short edge of pastry. Top with 1/4 cup cheese. Fold sides over chicken, then roll up. Brush with melted butter.
Place on an ungreased baking sheet. Repeat with remaining ingredients. Bake, uncovered, at 350° for 30-35 minutes or until phyllo dough is golden brown.