01 - Preheat the grill to medium-high heat, approximately 400°F (200°C).
02 - Pat chicken breasts dry. In a small bowl, combine olive oil, smoked paprika, garlic powder, onion powder, salt, and black pepper. Rub mixture thoroughly over both sides of chicken.
03 - Brush corn with melted butter and season all sides with salt and black pepper.
04 - Place chicken on hot grill. Cook for 6–7 minutes per side. During the last 3–4 minutes on each side, baste with barbecue sauce. Grill until chicken is cooked through and internal temperature reaches 165°F (74°C).
05 - While chicken cooks, grill corn on the cob. Turn occasionally until kernels are browned and tender, about 10–12 minutes total.
06 - Remove chicken from the grill and let rest for 5 minutes before slicing.
07 - Arrange grilled chicken and corn on plates. Garnish with chopped fresh parsley and lime wedges if desired.