In a medium bowl, whisk together 1 cup barbecue sauce and 1 1/4 tsp salt. Pour the sauce onto the chicken, press out the air, then toss the chicken to coat completely with the marinade.
Refrigerate overnight, or for at least 8 hours.
Before you grill, set the chicken out for at least an hour to come to room temperature.
Broil under high for 3-4 minutes per side or grill on medium-high and cook for 3-4 minutes per side. When you flip the chicken, brush with the remaining 1/4 cup of barbecue sauce.
Remove from heat and allow to rest for about 5 minutes before serving.