Place the wine and garlic into a large pan, bring to the boil and boil for about five minutes, until slightly reduced.
Add the cream and bring to a simmer, then stir in the cheese until melted. Stir in the chopped chives and transfer to a serving bowl.
Bring a large pan of water to the boil and cook the potatoes until tender, about 10-12 minutes. Thread the potatoes onto wooden skewers and serve with the fondue.