Preheat the oven to 400°. In a medium skillet, heat the vegetable oil until shimmering. Season the lamb with salt and pepper. Add the lamb to the skillet, fat side down, and cook over moderately high heat until richly browned, about 3 minutes. Turn the lamb fat side up and cook for 2 minutes longer. Transfer the skillet to the oven and roast the rack for about 20 minutes, until an instant-read thermometer inserted in the center of the meat registers 125° for medium-rare meat. Transfer the lamb to a carving board and let rest for 10 minutes.
Discard the fat in the skillet. Add the tangerine zest and juice and the chile to the skillet and boil over moderately high heat until the juice is reduced by half, about 2 minutes. Add the stock and boil until reduced by one-fourth, about 1 minute. Remove the skillet from the heat and swirl in the butter, 1 tablespoon at a time. Season the sauce with salt and pepper.
Carve the lamb into chops and arrange on warmed plates. Spoon the sauce over the lamb and serve.
When pairing wine with meat, always consider the flavors that are in the sauce. A Tuscan Sangiovese has the earthiness, dried-fruit notes and juiciness to go with this pan sauce.