Take out and throw away giblets and neck from chicken. Run chicken up cold water and dry well. Cut off any excess fat from chicken. Lay chicken breast side down on a cutting board and slice chicken in half lengthwise along the backbone, cutting to, but not through the other side. Flip chicken over. Beginning at the neck, separate skin from breast and drumsticks by inserting fingers and pushing between skin and meat. Lay chicken, breast side up in a shallow baking dish.
Mix together buttermilk, rosemary, salt, hot pepper sauce, and garlic. Spoon mixture between meat and skin and over top of chicken. Wrap chicken and chill for 24 hours.
Preheat grill to medium-high using both burners. After hot, switch off left burner.
Lay chicken skin side down on cooking spray coated grill rack, over left side. Shut lid and grill 1 1/2 hours or until meat thermometer reads 180 degrees F; turn chicken a half turn after 45 minutes. Take off skin and throw away before serving.