In a large shallow dish arrange the chicken pieces and pour the milk over the chicken. Allow to stand for 15 minutes. In a large bowl combine the flour, paprika, salt and pepper. Dredge the chicken pieces in the flour mixture, firmly patting the flour mixture onto the chicken and let sit in the flour mixture. Redredge the chicken pieces every few minutes with remaining flour mixture until thickly coated.
In a 12-inch heavy skillet, 2 inches deep, heat the oils to 375 degrees F. Carefully arrange as many pieces of chicken in the skillet as will fit in one layer. Cover the skillet, reduce the heat to low and cook the dark meat for 12 minutes and the white meat for 6 to 8 minutes, turning each piece once, or until a sharp fork slides out easily when inserted into the chicken pieces. Uncover the chicken, turn the heat up to high and cook for another 3 to 5 minutes or until it is deep golden brown. Transfer chicken to paper towels to drain. If necessary, cook remaining chicken in same manner. Serve the chicken warm.
Adapted from a recipe by Laurie Colwin as printed in Gourmet Magazine