01 - Preheat 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. Evenly coat both sides of chicken with the seasoning blend.
03 - Brush husked corn with melted butter and season with salt and black pepper according to preference.
04 - Place chicken breasts on the grill. Cook 6 to 7 minutes per side. During the final 3 to 4 minutes of grilling each side, baste chicken with barbecue sauce. Cook until internal temperature reaches 165°F.
05 - While chicken cooks, grill corn, turning occasionally, until evenly browned and tender, about 10 to 12 minutes.
06 - Remove chicken and corn from grill. Let chicken rest for 5 minutes before slicing to retain juices.
07 - Arrange grilled chicken and corn on serving plates. Top with chopped parsley and serve with lime wedges if desired.