Preheat the oven to 350°. In a large bowl, toss the bread cubes with the olive oil, capers, raisins, Swiss chard, shallots, garlic and thyme. Season with salt and black pepper. Spread the bread in a large enameled cast-iron casserole.
Season the chicken pieces with salt and pepper and arrange them over the bread. Cover the chicken with a piece of parchment paper and close the casserole with a heavy lid. Bake the chicken for 35 minutes.
Remove the lid and parchment paper and increase the oven temperature to 400°. Bake the chicken for 10 to 12 minutes longer, or until golden on top and cooked through. Remove the casserole from the oven and let stand for 5 to 10 minutes. Serve the chicken with the bread and greens.