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. Coat both sides of chicken thoroughly with the seasoning mixture.
03 - Brush husked corn with melted butter and season with salt and black pepper to taste.
04 - Place seasoned chicken breasts on the grill. Cook for 6 to 7 minutes on each side. Brush barbecue sauce on chicken during the last 3 to 4 minutes per side, continuing until internal temperature reaches 165°F.
05 - Grill corn cobs simultaneously, turning occasionally until tender and lightly charred, about 10 to 12 minutes.
06 - Remove chicken and corn from the grill. Allow chicken to rest for 5 minutes before slicing.
07 - Arrange grilled chicken and corn on plates. Garnish with chopped parsley and lime wedges if desired.