Heat gas or charcoal grill. Cut 18x12-inch sheet of heavy-duty foil. Place potatoes and carrots on center of foil sheet. Drizzle with butter. Sprinkle with Italian seasoning, peppered seasoned salt and cheese; stir slightly to mix and coat vegetables. Bring up 2 sides of foil so edges meet. Seal edges, making tight 1/2-inch fold; fold again, allowing space for heat circulation and expansion.
Place packet, seam side up, on grill over medium heat. Cover grill; cook 35 to 40 minutes or until vegetables are tender.
Open packet carefully to allow steam to escape. Sprinkle with chives.