Combine salt, brown sugar, paprika, cayenne pepper and olive oil in a small bowl and whisk to combine. Place chicken breasts in a 1-gallon zip-top bag. Pour marinade over top, close bag and turn chicken breasts until evenly coated in the mixture. Place bag in the refrigerator for at least 30 minutes.
Lightly oil the grill grate. Grill chicken over indirect heat for 18 to 20 minutes, turning occasionally, or until juices run clear. Watch carefully to prevent burning. Serve with Bush's Country Style Baked Beans.