Rinse chicken; pat dry with paper towels. Place each chicken breast half between 2 pieces of plastic wrap. Pound lightly until about 1/4 inch thick. Sprinkle with pepper.
Divide the cheese into 4 equal pieces; form into balls. Place a cheese ball in the center of each piece of chicken. Fold in the sides and roll the pieces up, jelly-roll style.
Line a baking sheet with parchment paper or foil. Evenly stack 8 phyllo dough sheets on a work surface. (Cover and return the remaining phyllo to your freezer.) With a sharp knife, cut the phyllo stack into 12-inch squares; discard trimmings.
Generously brush one square with butter. Place another square on top; brush with butter. Keep the remaining 6 squares of phyllo covered with plastic wrap to prevent drying.
Place a chicken breast, seam side down, on the buttered stack. Gather up the phyllo to form a bundle, twisting top slightly to hold it together. With a spatula, transfer to a prepared baking sheet. Repeat with the remaining phyllo squares and chicken breasts.
Bake in a 375 degree F oven for 25 to 30 minutes or until phyllo is golden. Serve with hot cooked wild rice, if you like.