Bring your offset smoker to temperature – You will want to maintain a temperature of roughly 250 degrees throughout the entire smoking process.
Prepare the chicken leg quarter – Bring the chicken to room temperature. Pat the chicken dry with paper towels, and remove any excess skin. You will find that there is often quite a bit of extra skin to remove from a chicken leg quarter.
Prepare the glaze – In a medium size bowl, thoroughly mix the honey chipotle glaze ingredients with a whisk. Optionally, you can place all the ingredients in a blender.
Brush the chicken – With a kitchen brush, liberally brush the glaze over the front side of the chicken. Do this a few times to ensure that the entire chicken is covered with the glaze.
Place the chicken onto the offset smoker – Place chicken on the 8” x 10” wire oven rack and place it into your offset smoker grill grate. Smoke until the internal temperature of the chicken reaches 165 degrees, about 2 hours. As a chicken leg quarter is usually larger and thicker than a regular thigh or breast, the smoking time will be longer.
Remove the chicken from the offset smoker – Let the chicken rest for 10 minutes before carving. Cut the chicken between the drumstick and the thigh. This should serve one person.