Place the beets, potatoes, and carrot into a saucepan, fill with water, and bring to a boil. Reduce heat and simmer until tender, about 20 minutes.
Remove vegetables and allow to cool; peel the beets and potatoes. Dice the beets, potatoes, and carrot, and place into a salad bowl. Stir in onion, pickle, sauerkraut, olive oil, and salt. Chill the salad for 2 to 3 hours; serve cold.