In a Dutch oven, cook the bacon until nice and crispy. Remove the bacon to a paper towel-lined plate to drain and crumble when cooled.
Pat the chicken dry and season on all sides with salt and pepper. Sear the chicken on all sides in the pan with the rendered bacon fat, until the outside is brown and crispy. Remove the chicken to a plate and add the fennel to the pan. Season with salt and pepper, to taste, and saute until caramelized and tender, about 10 minutes. Add a little water if the fennel starts to burn. Pour in the beer and bring it to a simmer. Nestle the chicken and all resting juices, breast side down, in the fennel and beer. Cover and transfer the pan to the oven. Roast for 35 to 45 minutes, flipping the chicken over after 20 minutes.
Remove the pan from the oven and put over low heat. Remove the chicken pieces to a warmed serving platter. Add the vinegar to the sauce and simmer to reduce to a thicker consistency, about 5 minutes. Pour the sauce over the chicken pieces, top with crumbled bacon and serve immediately. If you want a smoother sauce, just strain the sauce after it has reduced.