Pre-heat oven to low.
Line baking sheet with paper towels.
Pour oil into a large, heavy skillet to a depth of 1 inch.
Heat the oil over a high heat of 375 degrees (or until a small cube of fresh bread sizzles instantly when added to the oil).
Add the chicken thigh and leg pieces to the skillet first.
Adjust the heat so that the temperature remains between 340 and 350 degrees (or until a small cube of bread sizzles slowly when added).
Fry chicken until golden brown and cooked through, turning chicken occasionally, about 15 minutes.
Using tongs, transfer the chicken to paper towel-lined baking sheets.
Place baking sheet with chicken in the pre-heated oven to keep warm while frying the remaining chicken.
Reheat the oil back up to 375 degrees.
Add the chicken breast and wing pieces to the skillet.
Adjust the heat so that the temperature is between 340 and 350 degrees.
Fry the chicken until cooked through and golden brown, about 10 minutes, turning occasionally with tongs.
Using tongs, transfer chicken to another prepared baking sheet and drain.
Place in the oven to stay warm until ready to serve.