01 - Preheat grill to medium-high heat, approximately 400°F.
02 - Pat chicken breasts dry. In a small mixing bowl, combine olive oil, smoked paprika, garlic powder, onion powder, salt, and black pepper. Evenly rub the mixture over both sides of the chicken breasts.
03 - Brush ears of corn with melted butter and season with salt and black pepper.
04 - Place chicken on the grill and cook for 6 to 7 minutes per side. During the last 3 to 4 minutes on each side, baste with barbecue sauce until fully cooked and internal temperature reaches 165°F.
05 - While chicken cooks, place corn on the grill. Grill, turning 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 - Arrange grilled chicken and corn on serving plates. Garnish with chopped parsley and lime wedges, if desired.