Preheat the oven to 275 degrees F.
salt and pepper the chuck roast.
Heat the olive oil in large pot or Dutch oven over medium-high heat. Add the halved onions to the pot, browning them on both sides. Remove the onions to a plate.
If needed, add a bit more olive oil to the very hot pot. Place the meat in the pot and sear it for about a minute on all sides until it is nice and brown all over. Remove the roast to a plate.
With the burner still on high, use red wine to deglaze the pot, scraping the bottom with a whisk. Stir in the horseradish. Place the roast back into the pot and add the beef stock to cover the meat halfway.
Add in the onions and the carrots, and the potatoes.
Put the lid on, then roast for 3 hours for a 3-pound roast. For a 4 to 5-pound roast, plan on 4 hours. The roast is ready when it's fall-apart tender.