01 - Preheat grill to medium-high heat, approximately 400°F.
02 - Pat chicken breasts dry. In a small bowl, combine olive oil, smoked paprika, garlic powder, onion powder, salt, and black pepper. Evenly rub the seasoning mixture on both sides of each chicken breast.
03 - Brush each corn cob with melted butter and season all over with salt and black pepper.
04 - Place seasoned chicken breasts on preheated grill. Cook for 6 to 7 minutes per side. During the last 3 to 4 minutes on each side, baste with barbecue sauce. Continue grilling until internal temperature reaches 165°F.
05 - While chicken cooks, grill corn, turning occasionally, until lightly charred and tender, about 10 to 12 minutes.
06 - Transfer chicken and corn from grill. Allow chicken to rest for 5 minutes before slicing.
07 - Arrange sliced grilled chicken and corn on plates. Garnish with chopped parsley and lime wedges if desired.