Pound the chicken breasts to an even thickness for quick and even grilling.
In a bowl, whisk together olive oil, apple cider vinegar, smoked paprika, garlic powder, salt, and pepper.
Place chicken in a zip-top bag or shallow dish and pour marinade over it. Refrigerate for at least 30 minutes.
Preheat your grill to medium-high heat. Lightly oil the grates.
Grill chicken for 5-7 minutes on each side or until internal temperature reaches 165°F (75°C).
Let the chicken rest for a few minutes before assembling the sandwiches.
Toast buns lightly on the grill if desired.
Assemble sandwiches with lettuce, tomato, grilled chicken, onion, and a drizzle of BBQ sauce.