In a large resealable plastic bag, combine the chicken breasts with the pickle juice and a generous pinch of ground pepper. Seal the bag, pressing out any air, and refrigerate overnight.

Preheat the oven to 325 degrees. Season the chicken legs with salt and pepper. Heat 1 tablespoon of the olive oil in a medium enameled cast-iron casserole. Add the chicken legs and cook over moderate heat, turning once, until browned, about 12 minutes. Transfer the chicken to a plate. Add the onions, carrots, and celery to the casserole and cook over moderate heat, stirring, until softened, about 7 minutes. Add the wine, bay leaves, and peppercorns.

Return the chicken legs to the casserole. Add the stock and bring to a boil. Cover and braise in the oven for about 1 hour, until the meat is very tender. Transfer the chicken legs to a plate to cool slightly. Pull the meat from the bones; discard the bones and skin. Strain the cooking liquid and wipe out the casserole. Return the cooking liquid to the pot and boil until the sauce is reduced to 1 cup, about 25 minutes; keep warm.

Meanwhile, raise the oven temperature to 350 degrees. Pat the chicken breasts dry. Heat 1 tablespoon of the oil in an ovenproof skillet. Add the breasts, skin side down, and cook over high heat until golden, about 6 minutes. Turn and cook for 2 minutes longer. Transfer the skillet to the oven and roast the chicken for about 25 minutes, until cooked through. Transfer the chicken breasts to a platter and let rest for 10 minutes.

Wipe out the skillet and heat the remaining 1/4 cup of olive oil until shimmering. Add the Swiss chard and garlic, season with salt and pepper, and cook over high heat, tossing, until tender, about 5 minutes. Stir in the shredded leg meat and half of the sauce. Spoon the chard and chicken onto plates and serve with the seared breasts. Drizzle the remaining sauce all around and serve right away.

The braised chicken legs can be refrigerated for up to 3 days.