01 - Set grill to medium-high heat, approximately 400°F.
02 - Pat chicken breasts dry. In a small bowl, blend olive oil, smoked paprika, garlic powder, onion powder, salt, and black pepper. Rub both sides of chicken with the spice mixture.
03 - Brush corn cobs with melted butter and season with salt and pepper according to preference.
04 - Position chicken breasts on the grill. Cook for 6–7 minutes per side. During the last 3–4 minutes on each side, baste generously with barbecue sauce. Grill until internal temperature reaches 165°F.
05 - While chicken grills, place corn on the grill. Cook, turning occasionally, for 10–12 minutes or until lightly charred and tender.
06 - Transfer grilled chicken and corn off the grill. Let chicken rest for 5 minutes before slicing. Serve with corn, garnishing with fresh parsley and lime wedges if desired.