1 (3 1/2-pound) chicken, cut into 8 serving pieces
1 pound onions or shallots, thinly sliced
1 head garlic, cloves separated and peeled
1/4 cup balsamic vinegar
Cook bacon in a deep, 12-inch, heavy skillet over moderately low heat, turning twice, until crisp, about 8 minutes. Transfer with a slotted spoon to paper towels to drain and reserve bacon fat in skillet.
While bacon is cooking, pat chicken dry and season with salt and pepper. Brown in bacon fat, beginning with skin side down, in 2 batches, over moderately high heat, turning, about 8 minutes. Transfer browned chicken with tongs to a plate, and pour off all but 2 tablespoons fat from skillet.
Lower heat, add onions to skillet and cook, covered, stirring occasionally, until soft and pale golden, about 10 minutes.
Remove lid and cook onions, stirring, until deep golden, about 10 minutes more. Add garlic and 1 cup water to skillet and boil, stirring, 1 minute.
Return chicken to skillet, turning pieces to coat, then arrange them skin sides up and gently simmer, covered, until chicken is cooked through and garlic is tender, about 30 minutes.
Transfer chicken with tongs to a serving dish. Add vinegar to sauce and boil, uncovered, mashing garlic with back of a spoon or a potato masher, until slightly thickened. Season sauce with salt and pepper and pour over chicken, then sprinkle with bacon.