Place the whole, unpeeled potatoes in a large pot and cover with cold, salted water.
Bring to a boil and cook until they are fork-tender, about 20-25 minutes.
Drain the potatoes and let them cool just enough so you can handle them safely.
While the potatoes are still warm, carefully peel off the skins.
Cut the warm potatoes into medium-sized dice, about ½-inch / 1. 5 cm, and place them in a large mixing bowl along with the minced onion.
In a small saucepan, gently heat the white wine vinegar and caraway seeds over low heat for 1-2 minutes until warm.
Do not let it boil. Immediately pour this warm vinegar mixture over the potatoes and onions. Gently toss to coat everything, allowing the warm potatoes to absorb the tangy dressing.
Drizzle the olive oil over the salad, then sprinkle with salt, pepper, and the fresh chives.
Toss gently one more time, being careful not to break up the potatoes.
Taste and adjust the seasoning as needed. You can serve the salad immediately while it's warm, or chill it for several hours for the flavors to meld even more. If serving chilled, let it sit at room temperature for 15 minutes and give it a final stir before serving.