How to Make It
Cut 6 long strips of zest from the oranges and 4 long strips from the limes. Peel the oranges and limes with a knife, removing all of the white pith. Working over a bowl, cut in between the membranes to release the orange and lime sections. Reserve 1/2 cup of juice.
Cut the breast meat from the bones, or have the butcher do this for you. Coarsely chop the bones. In a large ovenproof skillet, heat the vegetable oil. Add the bones and cook over high heat, turning occasionally, until browned, about 4 minutes. Add the onion, garlic and thyme and cook over moderate heat, stirring occasionally, until the onion is golden brown, 5 minutes. Add the wine and boil over high heat until reduced to 1/2 cup. Add the stock and the reserved zest strips and simmer over moderate heat until the stock has reduced by half, 10 minutes. Add the reserved citrus juice and simmer for 10 minutes longer. Strain the sauce into a saucepan and boil over high heat until reduced to 1 1/4 cups, 8 minutes. Wipe out the skillet.
Preheat the oven to 400°. Heat the olive oil in the skillet. Season the chicken breasts with salt and pepper and add them to the skillet skin side down. Cook the chicken over moderately high heat until the skin is browned, about 4 minutes. Turn the chicken over and roast in the oven for 10 minutes longer, until just cooked through. Transfer the chicken to plates.
Pour off the fat in the skillet. Add the citrus sauce and boil over high heat, scraping up any browned bits that have stuck to the bottom, until reduced to 1 cup, about 2 minutes. Add the reserved orange and lime sections and cook to warm through. Remove the skillet from the heat and gently stir in the butter. Season the sauce with salt and pepper. Spoon the citrus sauce and citrus sections over the chicken breasts and serve right away.