In a small bowl or measuring cup, combine the buttermilk, garlic, paprika, 1½ teaspoons salt, and ¾ teaspoon pepper.
Divide the buttermilk mixture and chicken between 2 large resealable plastic bags. Let marinate in the refrigerator, turning the bags occasionally, for at least 1 hour and up to overnight.
Heat grill to medium-low. Remove the chicken from the marinade (discard the marinade) and grill, covered, turning occasionally, until cooked through, 30 to 40 minutes.