Place the chuck roast in the slow cooker. Add the diced onion, carrots, garlic cloves, tomato paste, beef stock, red wine, salt, and pepper. Stir to combine everything, making sure the roast is coated in the liquids and seasonings. Set the slow cooker to low and let it cook for 4 hours.
3 pounds chuck roast, 1 onion, 3 carrots, 4 garlic cloves, 2 tablespoons tomato paste, 1 cup beef stock, 1 cup red wine