Place the goat cheese in a small saucepan over low heat. Pour in the heavy cream and white wine, then add the thyme leaves and some black pepper. Cook, stirring occasionally, until the cheese is melted and the wine has cooked off, 8 to 10 minutes. The fondue will be thick and creamy. Remove from the heat and stir in the chives.
Drizzle the honey over the fondue and serve warm with apples, grapes and sourdough bread for dipping.