Preheat the oven to 450 degrees F. Line a baking sheet with aluminum foil (using foil makes for a faster clean up).
Pat the chicken completely dry so that the butter will stick. Using a pair of kitchen shears, cut out the back bone by cutting down each side of it to remove. Turn the chicken over and lay it out flat on the cutting board. Using both hands, press down firmly on the chicken breast to break the breast bone and flatten the chicken as best you can. Tuck the wing tips behind the wings.
Put the chicken on the prepared baking sheet. Rub the entire skin with the butter, then sprinkle on the smoked paprika, salt and pepper and rub it in.
Roast until a meat thermometer reads 160 degrees F, 35 to 45 minutes. Let rest before carving.