Tear off 4 (18- x 12-inch) sheets of aluminum foil; lightly grease 1 side of each sheet.
Place 1 chicken breast in center on lightly greased side of each foil sheet. Brush both sides of chicken evenly with oil; sprinkle evenly with salt and pepper. Spoon salsa evenly over chicken. Top evenly with black beans and, if desired, corn.
Bring together 2 sides of each foil sheet over ingredients, and double fold with about 1-inch-wide folds. Double fold each end to form a packet, leaving room for heat circulation inside packet. Place packets on a baking sheet.
Bake at 450° for 20 minutes. Carefully open foil packets to prevent burns from hot steam. Sprinkle evenly with cheese before serving. Serve chicken with desired toppings.