01 - Preheat grill to medium-high heat, approximately 400°F.
02 - Pat chicken breasts dry. Combine olive oil, smoked paprika, garlic powder, onion powder, salt, and black pepper in a small mixing bowl. Rub the seasoning mixture over both sides of the chicken breasts.
03 - Brush husked corn with melted butter and season evenly with salt and 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 and continue grilling until internal temperature reaches 165°F.
05 - While chicken is grilling, place corn on grill, turning occasionally, and cook until kernels are browned and tender, about 10 to 12 minutes.
06 - Remove chicken and corn from 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.