Heat a large skillet over medium-high heat. Add corned beef and cook until crisp on all sides, about 5 minutes.
Place drained sauerkraut in a bowl with caraway seed; stir to combine.
Set an oven rack about 6 inches from the heat source and preheat the oven's broiler to high.
Place 1/2 of the chips in an oven-proof skillet. Scatter 1/2 of the corned beef and 1/2 of the sauerkraut on top of the chips. Drizzle 1/2 of the Thousand Island dressing over the corned beef and top with 1/2 of the Swiss cheese. Repeat layers once more.
Broil in the preheated oven until cheese has melted, about 5 minutes.