Stir the buttermilk, garlic, paprika, salt and pepper together in a mixing bowl.,
Place the chicken in a zippered plastic bag and pour the buttermilk mixture into it. Now take the rosemary and roll it between the palms of your hands (this releases the oils) and drop it into the bag. Seal up the bag and let it marinate in the refrigerator, turning the bags occasionally, for at least 4 hours and up to overnight.
Heat grill to medium high. Remove the chicken from the marinade (throw the marinade out) and grill until cooked through, about 20 to 30 minutes. Turn the chicken over a few times as you grill. This chicken is terrific hot off the grill or chilled!