Preheat your smoker to 275 °F.
In a small bowl, mix together the salt, paprika, garlic powder, and black pepper.
Pat the chicken dry with paper towels to get rid of any excess liquid. Place them on a tray.
Use a basting brush to brush both sides of the quarters with the olive oil.
Rub the seasoning on both sides of the chicken - on and under the skin (if you can).
Place the chicken, skin side up, directly onto the smoker grates.
Smoke for 1.5 - 2.25 hours or until an internal temperature reaches 185 °F to 190 °F (it's safe at 165 °F but extra tender at 185-190!).
Remove the quarters from the smoker and let them rest for 5 minutes.
Let any leftovers cool completely. Refrigerate in an airtight container for up to 4 days.
You can reheat them skin-side up on the grill. It takes 10-15 minutes over medium heat to warm them up. Turn them after about 8 minutes to crisp the other side up. You can also reheat in the oven at 350 °F (175 °C) for 15-20 minutes. You can turn on the broiler for the last few minutes to get the skin crisper.
