Preheat the oven to 400°F. Wrap 3 of the beets in foil and place on a small baking sheet. Roast until tender, about 1 hour. Let cool, then unwrap beets and rub off skins with a paper towel. Halve and thinly slice.
Meanwhile, coarsely chop remaining 3 beets and place in a large saucepan. Add broth, onion and caraway seeds. Bring to a boil, lower heat and cook at a gentle simmer for 50 minutes, or until broth is deeply colored and beets are very tender. Strain broth and discard solids. Wipe out the pan, then return broth to the pan.
Add reserved sliced beets to the pan and stir in vinegar, salt and sugar. Reheat if necessary and serve sprinkled with dill and chives. Serve and enjoy!