Brown the chestnuts. Add 1 tablespoon of the butter to a large pot fitted with a lid (a Dutch oven is perfect). Over medium heat, melt the butter to coat the bottom of the pot. Over medium-high heat, add the roasted, peeled chestnuts and sauté them until they are golden brown, about 5 minutes.
Add the onions. Add the peeled pearl onions and stir to combine. If the bottom of the pan is dry, add about 1 tablespoon of olive oil. Sauté for another 5 minutes or so, until the onions are slightly tender and golden brown.
Add thyme and liquids and simmer. Add the thyme, stock, and red wine and bring to a boil. Then turn the heat to low, cover the pot, and simmer for 10 minutes.
Reduce the liquid. Remove the lid, and turn the heat to medium-low. Cook to reduce the liquid until all but about 3 tablespoons remain, about 20 minutes. (Gently stir the mixture from time to time during the cooking process. Cooking times may vary.)
Add remaining ingredients. Stir in the balsamic vinegar, pecans, sugar, and the remaining 3 tablespoons of butter. Season to taste with salt and pepper. Serve!