Heat a grill over medium-high heat and clean and lightly oil the hot grates.
Season the chicken breasts with salt and pepper and place on the grill. Grill the breast for 5 minutes, then flip, brush with some of the barbecue sauce, and continue to grill until cooked through, 5-7 minutes more.
Transfer the chicken to a plate and set aside to cool slightly.
Use 2 forks to shred the chicken, add to a bowl, and toss with the remaining barbecue sauce.