01 - Set the grill to medium-high heat, approximately 400°F.
02 - Pat chicken breasts dry with paper towels. In a small bowl, combine olive oil, smoked paprika, garlic powder, onion powder, salt, and black pepper. Evenly coat both sides of the chicken with the mixture.
03 - Brush husked corn on the cob with melted butter and season with salt and black pepper to preference.
04 - Place chicken breasts on the grill. Cook for 6 to 7 minutes per side. During the final 3 to 4 minutes of grilling on each side, baste generously with barbecue sauce. Continue grilling until internal temperature reaches 165°F.
05 - Place corn alongside chicken and grill, turning occasionally, until kernels are browned in spots and tender, about 10 to 12 minutes.
06 - Remove chicken and corn from the grill. Let chicken rest for 5 minutes before slicing to retain juices.
07 - Serve sliced chicken with grilled corn on the cob. Garnish with chopped parsley and lime wedges if desired.