Preheat oven to 400° F. Slice the potatoes very thin (no more than 1/8 inch), grate the cheese, chop the chives, and mince the garlic. Butter the dish and cover the bottom with a layer of overlapping potato slices. Dot with butter, season with salt and pepper, and cover with cheese and chives. Repeat with two more layers.

Bring the cream to a simmer in a small pot with the garlic and thicken slightly. Pour the cream over the potatoes and bake until tender and golden brown on top, about 45 minutes, covering with aluminum foil as necessary to prevent burning.