Most potato gratins are based on cream, but chicken stock is substituted here, lowering the calorie count. Russet potatoes are a good choice because they have a high starch content, which helps to thicken the liquid.
Position a rack in the lower third of the oven, and preheat to 375 F. Lightly butter a 9 x 13-inch (3-quart) baking pan and set aside.
Place a layer of potato slices in the prepared pan, overlapping each row of slices by about a third. Sprinkle with salt and pepper. Cover with another layer of potato slices.
Mix the Cheddar and Swiss cheeses in a small bowl. Sprinkle a layer of the cheese mixture over the potatoes. Top with a layer of potatoes and season with salt and pepper. Repeat, then top with more cheese. Continue in this manner until you have used all of the potatoes and cheese.
Pour the hot chicken stock into the pan. Cover the pan tightly with aluminum foil and transfer to the oven. Bake for 45 minutes, then remove the foil and continue cooking until the potatoes are tender when pierced and the cheese is golden, 15 to 25 minutes. Let rest 10 minutes before cutting and serving.