Season chicken with salt and pepper.
Coat with some of the flour, then dip in buttermilk; coat again with remaining flour.
Pour cooking oil into deep skillet to depth of 1 1/4 inches; heat to 350°.
Regulate heat so chicken fries at 325°.
Fry, a few pieces at a time, in hot oil till tender, 12 to 15 minutes; turn once.