Chicken Leg Quarters  

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The breast and wings are the most popular pieces of meat on a chicken, but if you plan to smoke your chicken, the dark meat is by far your best choice.
Chicken Leg Quarters is where it’s at! Not only do legs and thighs have more flavor than their counterparts but they’re also more forgiving when it comes to cooking. If you over cook a breast on the smoker or grill, you can forget it. There’s no amount of sauce that will save you, but legs & thighs stay juicy even if you overshoot the temperature by 10 degrees. They are by far your best bet for a long, low and slow smoke.

Note:
If time permits, it is highly advisable to soak your chicken in a brine for a few hours to overnight before applying the rub.
See PaPa's Brine for chicken recipe.

Ingredients:
4 to 6 Chicken Leg Quarters
Ingredients for the rub
Your favorite BBQ sauce

Rub:
(This will make approximately 1 cup of rub. Enough for about 4 to 6 leg quarters.)
 4 Tablespoons Sea Salt
4 Tablespoons black pepper
2 Tablespoon paprika
2 Tablespoons Garlic Powder
 2 Tablespoons ground red pepper (Optional)
Preferred wood:
Apple or Pecan

 Preparation:
Combine all rub ingredients in a small bowl and mix well or you can apply spices one at the time to suite your own taste.
Apply spice rub evenly to leg quarters.
Wrap the prepared chicken tightly and place in your favorite non-reactive container (Tupperware), and place in the refrigerator.
Allow it to rest for at least 1 hour but preferable over night.
Take the meat out about an hour prior to cooking so it can reach room temperature. This will help considerably to shorten the smoking time.
Smoking:
Preheat the smoker to 275 degrees.
Place the Leg Quarters skin side up on the rack and smoke for approximately 1 hour.
After an hour, the skin should have started to get some color and firm up a bit.
It’s a good idea to check the internal temperature here.
Continue to cook to an internal of 175 to 180 degrees.
If you plan to use a traditional BBQ sauce, it can be applied now.
Allow the chicken to cook and additional 15 minutes or so to let the sauce set up.

This is where the Alabama White Sauce comes into play. It’s a mayonnaise based sauce with a touch of vinegar and a little heat. 
White BBQ Sauce:
 2 cups mayonnaise
 1 cup distilled white vinegar
1/2 cup apple juice
2 teaspoons prepared horseradish
2 teaspoons ground black pepper
2 teaspoons fresh lemon juice
1 teaspoon salt
1/2 teaspoon cayenne pepper
Whisk the above ingredients in a large bowl and drizzle over the chicken just before serving.
It makes enough sauce for 8-10 Chicken Quarters.

Can be finished on a hot grill "Before Applying Sauce" if you want to crisp the skin up a little more.