Place the pan on high heat, and using a deep-frying thermometer, heat the oil to 360 degrees.
In the meantime, pour the flour into a plastic or paper bag. Place the chicken in the bag and shake to completely coat the pieces with flour. Remove chicken and dust off any excess flour.
When the surface of the oil is rippling and the thermometer registers 360 degrees, add several pieces of the chicken at a time, beginning first with the legs and thighs, then the wings. Don't overcrowd the pan.
Fry the chicken until it is golden brown and juices run clear when a piece is pierced with a fork. The thighs and legs should cook in 20 to 25 minutes, the wings in 18 to 20 minutes.
If the temperature drops below 360 degrees, let the oil heat back up before adding more chicken. Remove the chicken from the hot oil and drain on paper toweling. Keep warm in a 200-degree oven.
Variation: Many Southern cooks say that the special trick to crispy fried chicken is that the pan has to be covered during part of the cooking period. My sister favored this method, which can be tricky, but does produce a crackling-like skin. For best results, heat the oil to about 350 degrees, add a few pieces of chicken, cover the pan, lower the temperature a bit, and cook the chicken covered for 5 minutes. Remove the cover, turn over the chicken and cook, covered, for 5 more minutes.