I brine them for an hour then wrap them in bacon and smoke them in Mesquite. You might have to reverse-sear them to crisp the bacon. Here's the brine and its source:
"The following is a tried and tested chicken brine recipe.
1 gallon water
3/4 cup kosher salt
2/3 cup sugar
3/4 cup soy sauce
1 teaspoon each of dried tarragon, thyme, black pepper
1/4 cup olive oil
Start by boiling the water and then adding the salt and sugar, so that it will dissolve easier. Then add the spices to the hot liquid so that the flavors are extracted. Cool the brine solution.
Place the brine solution into a non-reactive container and immerse the chicken in the brine, weighting it down if necessary. (Use a heavy plate or a brick inside a ziploc bag as a weight). Place the container into the refrigerator and leave for 10 hours. You can also brine the chicken in an ice chest, by pouring the brine solution into the ice chest, immersing the chicken and weighting down. (Use ziploc bags filled with ice cubes, or "blue ice" to keep the brining solution cool during the brining process.
Upon completion of the brining time remove the chicken from the brine and wash twice for at least 30 seconds in fresh water. Dry the chicken with paper towels.
A few things that you need to be remember when brining:
1. Make sure your brine does not contain too much salt. The salty flavor of a brine is typically offset by using some kind of sweetening agent such as sugar, honey, maple syrup etc.
2. Do not leave the chicken in the brine for too long or you will end up with a very mushy and salty end product.
3. Make sure you wash the chicken in fresh water for 30 seconds, at least twice after you remove it from the brine.
4. Be careful about using acidic products in your brines as these will begin to ‘cook’ the meat and result in a mushy end product.
5. Brining must take place at temperatures of 40 degrees or below. Only place your chicken into the brining solution once it is cold. You can cool the brining solution in the refrigerator or by using ziploc bags filled with ice cubes.
6. Ensure that the brine solution completely covers the chicken during the brining process.
Some guidelines if you are not brining chicken halves are as follows:
* Chicken Parts 1 ½ hours
* Chicken Breasts 1 hour
* Cornish Game Hens 2 hours"
Source