How to Make It
Mash the butter and flour into a smooth paste in a small bowl; set aside.
Cook the bacon in a large pot or Dutch oven over medium-high heat, stirring frequently, until crisp, 6 to 8 minutes. Transfer to a plate with a slotted spoon; reserve the pot.
Season the chicken with 1 teaspoon salt and ¼ teaspoon pepper. Add the chicken to the reserved pot and cook, skin-side down, in 2 batches, until the skin is crisp, 6 to 8 minutes per batch. Transfer to a separate plate.
Pour off all but 3 tablespoons of the fat from the pot; reserve the pot. Reduce heat to medium. Add the shallots to the reserved pot and cook until golden brown, 4 to 6 minutes. Add the wine and cook until syrupy, 8 to 10 minutes. Add the broth and bring to a simmer. Whisk in the butter mixture.
Return the chicken to the pot, skin-side up. Simmer, uncovered, until an instant-read thermometer inserted into the thickest piece (avoiding the bone) registers 165° F, 25 to 35 minutes. Add the vinegar.
Serve the chicken with the chives and reserved bacon.