Peel the potatoes and slice them into thin 1/8-inch slices using a mandolin or sharp knife. Rinse the slices in several changes of water until the water runs clear. Drain them and pat them dry.
Put about 3 inches of oil into a large deep pot; it should not come up more than half way. Bring the oil up to 325 degrees F over medium-high heat. Working in batches, carefully add the potato slices, a dozen at a time. Stir them to make sure they are not sticking together. Fry until they are a golden brown, about 3 to 4 minutes. Remove and drain them well on paper towels; season with salt. Repeat with the remaining potato slices.
Heat the oven to 450 degrees F. Place a layer of the chips onto a baking dish and sprinkle with some of the bleu cheese and chives. Place another layer of chips onto that and some more cheese and chives. Continue until you have used up all the chips and cheese. Put into the oven and bake until the cheese has melted, about 5 minutes. Garnish with more chives.