01 - Preheat the grill to medium-high heat, approximately 400°F (200°C).
02 - Pat chicken breasts dry. Combine olive oil, smoked paprika, garlic powder, onion powder, salt, and ground black pepper in a small bowl. Rub the mixture evenly over both sides of the chicken breasts.
03 - Brush husked corn with melted butter. Lightly season with salt and ground black pepper.
04 - Place chicken breasts 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 is thoroughly cooked and reaches an internal temperature of 165°F (74°C).
05 - While the chicken cooks, grill the corn on the grill grates, turning occasionally until browned in spots and tender, about 10 to 12 minutes.
06 - Remove chicken and corn from the grill. Allow chicken breasts to rest for 5 minutes before slicing.
07 - Arrange sliced grilled chicken and corn on plates. Garnish with chopped parsley and lime wedges as desired.