1. In a medium bowl, cover wood chips (if using) in water. Let soak at least 30 minutes; drain just before using.
2. In a food processor, combine garlic, chili powder, thyme, rosemary, olive oil, salt, and pepper. Process until mixture forms a paste.
3. Rinse chicken inside and out; pat dry. Press down on the breastbone of the chicken to flatten the bird slightly; rub the paste evenly over all the skin.
4. Prepare your grill for indirect heat (see "How to set up your grill for indirect heat" below). The temperature inside your grill should be between 350° and 400° (insert a long-stemmed thermometer through lid vent to measure temperature). If using a gas grill, place all the chips in the metal smoking box or in a foil pan directly on the heat in a corner. If using a charcoal grill, scatter half of the wood chips over the coals.
5. Place the chicken over the drip pan, breast side down. Cover barbecue with lid. If using a charcoal grill, adjust vents so that they're open halfway. Cook 40 minutes, then turn the chicken over (if using charcoal, scatter another 20 briquets over coals, along with the remaining wood chips). Cover barbecue again.
6. Continue cooking chicken until a thermometer inserted through the thickest part of breast to bone reaches 170°, about 40 minutes longer. Transfer to a board or platter and let rest 10 minutes under a tent of foil. Carve to serve.
How to set up your grill for indirect heat.
On a charcoal barbecue: Ignite about 60 briquets on the firegrate of your barbecue. Let burn until coals are dotted with ash, about 25 minutes, then push coals to one side and lay a drip pan on the other side. Set grill in place.
On a gas barbecue: Turn heat to high and close lid for at least 10 minutes. Adjust heat to medium and turn off burners as needed to create a hot and a cool zone for indirect cooking. Set drip pan in cool zone; set grill in place.
Notes: Adding wood chips to the fire gives the chicken extra flavor.