01 - Preheat grill to medium-high heat (about 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. Thoroughly rub mixture over both sides of chicken breasts.
03 - Brush corn on the cob with melted butter and season with salt and black pepper.
04 - Place chicken onto hot grill. Cook for 6 to 7 minutes per side. During the last 3 to 4 minutes of grilling on each side, generously baste with barbecue sauce. Continue cooking until internal temperature reaches 165°F.
05 - While chicken grills, cook corn on the cob, turning every few minutes, until browned and tender, approximately 10 to 12 minutes.
06 - Remove chicken from grill and let rest for 5 minutes before slicing to retain juices.
07 - Arrange grilled chicken and corn on plates. Sprinkle with chopped parsley and serve with lime wedges as desired.