Heat 2 inches of oil in a deep-sided pan over medium to medium-high heat. Cut onions into 3/4- to 1-inch thick rings.
Whisk together the sour cream and buttermilk and season with salt, pepper and chives. Pour flour into a shallow dish and season it with salt and pepper as well. Double-coat the rings in buttermilk and flour. Add to hot oil and fry to crispy and golden, a few rings at a time.