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