Peel and wash the carrots and potatoes and cut them into small cubes. Peel and finely dice the onion. Heat oil in a pot. Brown carrots, potatoes and onion in it. Add vegetable stock, bring to the boil.
Cook the vegetables for about 20 minutes. Wash the meat and add to the vegetables about 15 minutes before the end of the cooking time. Take the meat out, let it cool down a bit and cut it into slices. Take out 1/3 of the vegetables, puree the rest of the vegetables in the broth.
Add chicken meat to the soup. Season to taste with salt and pepper. Add remaining vegetables. Wash the chives and, except for a few stalks for garnishing, cut into small rolls. Sprinkle carrot-potato soup with chives and garnish.
Add a dollop of sour cream.