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. Rub the mixture evenly over both sides of each chicken breast.
03 - Brush each ear of corn with melted butter and season with salt and black pepper.
04 - Place chicken breasts on grill. Cook for 6 to 7 minutes per side, basting with barbecue sauce during the last 3 to 4 minutes on each side, until the internal temperature reaches 165°F.
05 - While chicken cooks, grill the corn, turning occasionally, until browned and tender, about 10 to 12 minutes.
06 - Remove chicken and corn from 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.