Place the chicken in a large mixing bowl. Sprinkle with 1/4 cup salt and cover with cold water. Soak the chicken for 45 minutes.
Remove the chicken from the salt water and drain on paper towels.
Heat the shortening in an 8-inch cast iron skillet or a large deep skillet to about 360 degrees.
Sprinkle the chicken with 1 teaspoon salt and pepper. Coat each piece completely with flour, shake off the excess and gently place the chicken in the hot shortening. Fry 10 to 12 minutes per side or until golden brown, about 25 minutes total. Fry chicken in batches to prevent the skillet from becoming crowded.
Check the temperature of the oil occasionally. If the oil is too hot, the chicken will be too brown on the outside but not fully cooked through.
Drain fried chicken on a cooling rack placed over a rimmed baking sheet.