1. Rinse and pat dry chicken. Place chicken breast-side down on a cutting board. With kitchen shears or a very sharp boning knife, remove the backbone by cutting down either side. Turn chicken breast-side up and press firmly on the breast bone until you hear it crack and chicken lies just about flat. Rub the paprika, salt and pepper all over both sides of chicken.
2. Place chicken on the grill skin-side up; cook, flipping frequently and moving it to the cool area if you get flare-ups, until it is well-browned and cooked through, about 30 minutes. An instant-read thermometer inserted into the thickest part of the thigh and breast without touching bone should read 165°F. Transfer to a platter and let rest 10 minutes before carving.