Preheat your grill to medium-high heat.
In a small bowl, mix together the smoked paprika, garlic powder, onion powder, salt, and black pepper. Rub this spice mixture evenly over the chicken breasts.
In another bowl, combine the barbecue sauce, honey, apple cider vinegar, and olive oil. Stir until well blended. Reserve half of this mixture for basting and serving.
Place the seasoned chicken breasts on the grill. Cook for about 6-7 minutes on one side.
Flip the chicken breasts and brush the top with the reserved barbecue glaze. Grill for an additional 6-7 minutes, or until the internal temperature reaches 165°F.
Remove the chicken from the grill and let it rest for 5 minutes before slicing. Serve with the remaining barbecue glaze on the side.