Step 1Roast the chestnuts: Heat the oven to 350 degrees. With a small knife, score the chestnuts with an "X" on the flat side of the shell. Roast them on a baking sheet until the shells curl and darken where they have been scored, 25 to 30 minutes.
Step 2Remove the chestnuts from the oven and immediately cover them with a towel that has been soaked in ice water and wrung out. When the chestnuts are just cool enough to handle, peel away the shells and the thin skin covering the chestnut meat. Cut the chestnuts in quarters and set aside.
Step 3Trim the Brussels sprouts: Cut off the hard surface of the stem; remove any loose or yellowing leaves and cut a deep "X" in the base to allow the heat to penetrate to the center.
Step 4In a vegetable steamer, steam the Brussels sprouts, tightly covered, until they are just beginning to become tender, 6 to 7 minutes. They should still be slightly crisp at the center and bright green. Remove from the heat and set aside. (The dish can be made to this point up to 2 days in advance and the chestnuts and Brussels sprouts refrigerated tightly sealed.)
Step 5Cut the bacon crosswise into thin strips. In a dry medium skillet, cook the bacon over medium heat until the strips have rendered their fat and browned, about 6 to 8 minutes. Add the minced shallot and cook until it softens, about 2 to 3 minutes. Add the red wine vinegar and cook until it is reduced by half, about 1 1/2 minutes.
Step 6Add the Brussels sprouts and chestnuts to the skillet and toss to coat with the deglazed juices. Season to taste with one-fourth teaspoon salt and a pinch of black pepper and, if necessary, a little more red wine vinegar (the acidity pulls the flavors into focus). Serve immediately.