01 - Heat grill to medium-high (about 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 onto both sides of each chicken breast.
03 - Brush the corn with melted butter and sprinkle with salt and black pepper to taste.
04 - Place chicken on the grill and cook for 6 to 7 minutes per side. During the final 3 to 4 minutes of grilling on each side, baste the chicken with barbecue sauce. Continue cooking until the internal temperature reaches 165°F.
05 - While grilling the chicken, place the corn on the grill. Turn the cobs 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 parsley and lime wedges if desired.