Lay a small cooling rack over a large plate and set aside. (This will be where the cooked chicken is transferred to).
Rinse the pieces of chicken and set them on a large plate.
Sprinkle pepper and salt on each side of the chicken. Set aside.
Add flour to a shallow bowl and dredge a piece of the chicken in flour, or two pieces if your bowl is large enough. Generously coat the chicken in flour on all sides. Set aside for a moment.
Heat a large skillet on medium heat and add the oil so that it’s about ½ inch deep in the skillet. Depending on the diameter of the skillet you may need 1-½ to 2 cups of oil.
Sprinkle a tiny bit of the flour in the oil and if it sizzles add the pieces of flour-coated chicken to the oil (be careful not to crowd the pan). Continue to dredge as many pieces of chicken in the flour that will fit in the skillet without crowding. Depending on the size of the skillet, some of the chicken may need to be cooked in a second batch.
Using a cooking or carving fork, turn the chicken regularly as it turns a golden color. Try to poke the fork into the outside edges of the skin when turning the chicken rather than in the middle of the meat (so the juices don’t run out). When turning the chicken, a cooking fork tends to keep the crispy skin looking nicer than when using tongs.
If the oil starts to bubble quickly or splatter out of the skillet, turn the heat down just a bit. Keep an eye on the chicken to see if it’s turning a dark brown color (rather than a golden color) or cooking too quickly. If so, turn the heat down just a bit.
Continue to let the chicken cook until all sides are a medium to dark golden color and the chicken is thoroughly cooked. As the pieces of chicken are done cooking (about 30 to 40 minutes), remove them from the skillet and lay them on top of the cooling rack (that is laying on a large plate). The larger pieces of chicken like the breasts may take the longest time to cook.
Serve warm or cold right out of the fridge. Delicious served warm with mashed potatoes and gravy, or cold for lunch, or as a late night snack.