Preheat grill to medium-high heat, between 375° and 400° Fahrenheit.
While grill preheats, place 2 pounds boneless, skinless chicken breasts on large plate. Sprinkle 1 tablespoon BBQ dry rub and salt (optional) evenly over chicken breasts, seasoning all sides completely. Use more dry rub if desired.
Once grill has preheated to target temperature, spray grill grate lightly with neutral-flavored cooking spray. Place seasoned chicken breasts on grill grates over indirect heat.
Close grill lid and grill chicken, undisturbed, 4 to 5 minutes.
After 4 to 5 minutes, open grill and flip chicken breasts over. Close grill lid and grill chicken, undisturbed, 4 minutes more.
After 4 minutes, open grill lid and insert internal meat thermometer into thickest area of chicken breasts. If needed, continue grilling chicken until internal temperature reaches 160° Fahrenheit.
Once target internal temperature is reached, carefully transfer chicken breasts to cutting board. Immediately brush ½ cup BBQ sauce onto grilled chicken, dividing sauce evenly between both sides of each chicken breast. Set chicken aside to rest 5 minutes.