Mix the chili powder, paprika, salt, garlic powder and black pepper in a small bowl. Rub the mixture on all surfaces of the chicken.
Heat the butter and olive oil in the skillet. Add the chicken to the skillet and cook on the first side until the chicken is well browned, about 8 minutes.
Flip the chicken pieces and allow to cook for about 6 minutes. Top each piece with about half of barbecue sauce. Flip once more and coat the other side of the chicken with barbecue sauce. Cook until the chicken is cooked through.