01 - Preheat the grill to medium-high heat, approximately 400°F.
02 - Pat chicken breasts dry. In a small bowl, combine olive oil, smoked paprika, garlic powder, onion powder, salt, and black pepper. Rub mixture over both sides of chicken breasts.
03 - Brush corn with melted butter and season with salt and black pepper.
04 - Place chicken on the grill. Cook for 6 to 7 minutes per side. During the last 3 to 4 minutes of grilling per side, baste with barbecue sauce. Grill until chicken reaches an internal temperature of 165°F.
05 - While chicken cooks, grill corn on the cob, turning occasionally until browned and tender, about 10 to 12 minutes.
06 - Remove chicken and corn from the grill. Let chicken rest for 5 minutes before slicing.
07 - Serve grilled chicken with corn on the cob. Garnish with chopped parsley and lime wedges if desired.