The perfect grilled BBQ chicken that has you going back for "just one more piece" and leaves you with sticky fingers that require a trip to the sink for a proper washing before normal activities can be resumed.
Halve the chicken by removing the backbone and splitting the breastbone.
Evenly sprinkly the dry rub over the entire chicken and refrigerate overnight, or for at least 2 hours.
Remove the chicken from the refrigerator to bring it up to room temperature while you set up the grill for two-zone cooking with the direct side on medium-high.
Lightly oil the grill grates, then place the chicken skin-side down over direct heat with the lid closed until browned. Flip once, cooking about 5 to 7 minutes per side.
Move the chicken halves over to the indirect side of the grill with the breasts farthest from the direct heat and maintain a 400° F temperature with the lid closed.
After cooking for 20 minutes, use a heatproof basting brush to apply about ½ cup of BBQ sauce to both sides of the chicken (finishing with the skin side up).
After 10 more minutes, brush on ¼ cup more BBQ sauce.
Continue to cook until the internal temperature of the breasts reaches 160° F and thighs reach 175° F, about 20 minutes longer. There will be some carry-over cooking, which will raise the finished temperature another 5° or so. (Verify with a probe thermometer.)
Transfer the chicken to a cutting board to rest uncovered for 10 minutes before slicing and serving with more BBQ sauce.
There will be about 5° of carry-over cooking after the chicken is removed from the grill, so I like to pull the chicken when the breasts are 160°.