Smoked Chicken Prep time 15 mins Cook time 3 hours 1 whole chicken ¼ cup Steve’s BBQ rub Wash the chicken. Pat it dry with a paper towel. Rub the bird with Steve’s Basic BBQ Rub Smoke in the Bradley Smoker at 250F for 3 to 4 hours. Time may vary depending on outside temp, # of birds smoking, size of birds. The bird is done when the internal temperature of the bird reaches 165F in the thickest part of the breast.