In a bowl, whisk together buttermilk, garlic, salt, sugar, paprika and a generous amount of black pepper. Place chicken in a gallon-sized zip-top bag or lidded container and pour buttermilk brine over them. Make sure that all of the parts are covered. Refrigerate for a minimum of 2 and a maximum of 48 hours (24 hours being preferable).
Preheat oven to 425 degrees.
Line a baking dish with foil (for easiest clean-up). Remove chicken from buttermilk brine and place in the dish. Drizzle lightly with olive oil, sprinkle with additional paprika and salt.
Roast for 30 minutes for legs (approximately 35 to 40 minutes for breasts) until brown and a bit scorched in spots. (Or, alternatively, until the internal temperature of the meat reaches 165 degrees.)