01 - Preheat grill to medium-high, about 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 mixture evenly over both sides of chicken.
03 - Brush husked ears of corn with melted butter. Season corn with salt and black pepper to taste.
04 - Place chicken breasts on the grill. Cook for 6-7 minutes on each side, basting with barbecue sauce during the final 3-4 minutes per side. Grill until internal temperature reaches 165°F.
05 - While chicken cooks, grill corn on the cob, turning occasionally, until browned and tender, approximately 10-12 minutes.
06 - Remove chicken and corn from grill. Rest chicken for 5 minutes before slicing.
07 - Arrange grilled chicken and corn on plates. Garnish with chopped parsley and lime wedges if desired.