Brush the cooking grates clean. Drain 2 handfuls wood chips, add to the charcoal or the smoker box of a gas grill, and close the lid. When smoke appears, transfer the chicken-on-a-can to the grill, placing it over indirect medium heat. Close the lid and cook the chicken until the juices run clear when a thigh is pierced in the thickest part, or an instant-read thermometer inserted into the thickest part of the thigh (not touching the bone) registers 160° to 165°F, 1-1/4 to 1-1/2 hours. After the first 15 minutes, drain the remaining 2 handfuls wood chips and add to the charcoal or the smoker box. If using a charcoal grill, replenish the charcoal as needed to maintain the temperature, adding 6 to 10 unlit briquettes after 45 minutes. Leave the lid off the grill for 5 minutes to ignite the briquettes.