01 - Preheat the grill to medium-high heat, approximately 400°F.
02 - Pat chicken breasts dry. In a bowl, combine olive oil, smoked paprika, garlic powder, onion powder, salt, and black pepper. Rub the mixture thoroughly over both sides of the chicken.
03 - Brush each ear of corn with melted butter. Season evenly with salt and black pepper as desired.
04 - Place chicken on the grill. Cook for 6 to 7 minutes per side, basting with barbecue sauce during the last 3 to 4 minutes on each side. Grill until chicken reaches an internal temperature of 165°F.
05 - While chicken is cooking, grill the corn, turning occasionally, until browned and tender, about 10 to 12 minutes.
06 - Remove chicken and corn from the grill. Let the chicken rest for 5 minutes before slicing.
07 - Serve grilled chicken breasts alongside corn on the cob. Garnish with chopped parsley and lime wedges if desired.