01 - Bring grill to medium-high heat, approximately 400°F.
02 - Pat chicken breasts dry. In a small mixing bowl, combine olive oil, smoked paprika, garlic powder, onion powder, salt, and black pepper. Evenly rub the mixture over both sides of the chicken breasts.
03 - Brush corn cobs with melted butter and season with salt and black pepper as desired.
04 - Place chicken breasts on the grill. Cook 6 to 7 minutes per side, basting with barbecue sauce for the last 3 to 4 minutes on each side. Continue grilling until the internal temperature reaches 165°F.
05 - While chicken cooks, add corn to the grill. Turn occasionally and grill until golden and tender, about 10 to 12 minutes.
06 - Transfer chicken and corn from grill to a plate. Let the chicken rest for 5 minutes before slicing.
07 - Plate grilled chicken alongside corn on the cob. Garnish with chopped parsley and lime wedges if desired.