Heat a couple of inches of oil in a large deep frying pan over medium high heat or an electric fryer.
Mix the buttermilk and sour cream together, then soak the onion slices in it.
In a small shallow plate mix up the flour, chives, salt and pepper.
When the oil is hot enough, dip the onion slices one at a time into the flour and mix around to coat, then put the slice back into the buttermilk, then back into the flour for a double coating. Put in the hot oil and cook about 4-5 minutes, turning once, until golden on both sides. Don't fry too many at once. You don't want them touching.
Drain on paper towels or a rack.