01 - Preheat grill to medium-high heat, approximately 400°F.
02 - Blot chicken breasts dry with paper towels. Combine olive oil, smoked paprika, garlic powder, onion powder, salt, and black pepper in a small bowl. Evenly coat both sides of chicken breasts with the seasoning mixture.
03 - Brush each ear of corn evenly with melted butter and season with salt and black pepper.
04 - Arrange chicken breasts on the preheated 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 cooking until the chicken reaches an internal temperature of 165°F.
05 - While the chicken cooks, place corn on the grill. Rotate periodically and cook until evenly browned and tender, about 10 to 12 minutes.
06 - Transfer grilled chicken and corn to a platter. Allow chicken to rest for 5 minutes before slicing for optimal juiciness.
07 - Arrange sliced chicken and corn on plates. Garnish with chopped parsley and lime wedges if desired before serving.