Using a mandoline, slice the potatoes crosswise 1/8 inch thick. Arrange one-fourth of the potato slices in the prepared baking dish, overlapping them slightly. Sprinkle 1/4 cup of the cheese and 1 tablespoon of the chives over the potato slices. Repeat the layering two more times. Top with a final layer of potatoes and the remaining 1/4 cup of cheese. Pour the cream mixture over and around the potatoes.