Heat grill to medium-high. Season chicken breasts with salt and pepper. Clean and lightly oil hot grates. Place chicken on grill (if using skin-on chicken, place skin side down on grill).
Grill chicken, without turning, 6 to 10 minutes for boneless chicken and 10 to 14 minutes for bone-in. Flip and grill until cooked through, or a thermometer inserted in the thickest part of meat (avoiding bone) registers 160 degrees, 8 to 10 minutes more.
About 1 minute before chicken is done, brush with barbecue sauce.