In a bowl, combine all ingredients for the sauce, whisking thoroughly.
Add chicken to a gallon sized zippered bag and pour sauce contents over the top. Seal the bog (pressing out as much air as you can. Squidge sauce all over the chicken and then place in refrigerator to marinate for at least 4 hours (up to 24hours).
Based on your smokers own methods, prepare it to smoke at a temperature of 250degF.
Remove chicken from zippered bag and place in the smoker. Pour remaining sauce into a small sauce pan and place on stove over medium low heat and let simmer.
Allow chicken to smoke for 90 minutes. Then increase heat to 400degF. Baste each piece of chicken with simmered teriyaki sauce, then let cook for 15 minutes.
Turn each piece of chicken and baste again with sauce, let cook for 15 minutes more (or until center has achieved 165degF in the thickest part of the meat.
Baste the chicken on last time (on all sides) with sauce and then serve.