Preheat a large skillet over medium. Add oil, then swirl to coat pan.
Pound out chicken to an even thickness, and season with salt and pepper; add to hot skillet. Cook 5-6 minutes per side until golden or until center is no longer pink.
Chop cooked chicken into small pieces and toss into a bowl with BBQ Sauce. Shred carrots and lettuce.
Add BBQ chicken to the bottom portion of each bun, then top with lettuce and carrots; add tops of buns, forming 4 sandwiches.
Serve with grapes and raw green beans on the side.