Heat gas or charcoal grill. Cut 4 (18x12-inch) sheets of heavy-duty (or nonstick) foil. If using heavy-duty foil, spray foil with cooking spray.
In large bowl, gently mix potatoes, sausages and dressing. Spoon mixture evenly onto foil sheets. Wrap each packet securely using double-fold seals, allowing room for heat expansion.
When grill is heated, place foil packets on gas grill over medium heat or on charcoal grill over medium coals; cover grill. Cook 30 to 35 minutes, rotating and turning packets over several times, until potatoes are tender.
Remove packets from grill; open carefully to allow steam to escape. Sprinkle each with cheese and chives. Close packets; let stand until cheese is melted.