Cut potatoes into thin slices. Brush a baking dish with softened butter. Arrange potato slices in overlapping layers, seasoning each layer with salt and pepper.
Bring cream to a boil, add cheese and stir until melted. Pour mixture over potatoes. (Cream should not cover the potatoes, or it might boil over.) Bake potato gratin in an oven preheated to 180°C (approximately 350°F), about 50 minutes. Serve gratin sprinkled with chives.