We will be using an indirect cooking method for the chicken, which means if you're using a gas grill, only one of the burners will be on and the others will not. The wood chips will be set directly on the lit burners and the chicken will sit on the opposite side of the grill. Soak the wood chips for an hour in a container with 1/2 can beer and 1 cup water.
When wood chips have finished soaking, remove them from the soaking liquid and transfer to a smoker box. (If you don't have a smoker box, make a pouch out of heavy duty aluminum foil. Place the chips in the pouch and seal it, then use a sharp knife to poke holes all of the pouch. Set the smoker box/pouch directly over the burner that is your heat source. Turn on the grill to a medium high heat (about 350 degrees.) It will be ready to start cooking when white smoke is emitted from the grill.
Pour about 1 cup of the chipotle butter into a measuring cup. Use the needle to suck the chipotle mixture into the syringe. Start at the neck portion of the bird, injecting down under the skin and directly into the breast meat of the chicken. (You don't want to pierce the skin, because you want the flavors your injecting to remain inside the bird). Holding the bird upright, inject some marinade into the meatiest part of the thighs (you'll have to pierce the skin here, but keep the bird upright to mitigate the marinade seepage.
Sprinkle the outside of the bird with the rub and massage with your fingers.
Use a church key to puncture several holes in the top of the half empty beer can. Add about 1 tablespoon of rub to the beer. Carefully insert the beer can into the cavity of the chicken.
Place the chicken on the grill opposite the smoker basket and make sure that it's steady and won't fall over. Close the lid and cook for about an hour - or 1 hour and 15 minutes or when an internal thermometer registers 165 degrees. (I actually take it off a little before that because the chicken continues to cook when it's resting) Try not to open the grill too much in order to preserve the heat and smoke.
Preheat the oven to 425 degrees.
Add 1/2 cup of Stubb's Chipotle butter to a small bowl. Mix in the lime zest and honey. Set aside.
Place a potato on a large spoon (serving spoon will do, but it should cradle the bottom of the potato. Use a sharp knife to cut thin slices (about 1/8-1/4" thick) The edges of the spoon will prevent you from slicing all the way through the potato, creating that accordion effect. Divide the butter among the potatoes and massage on and slightly into the crevices -- not too much, you don't want to separate the slices. Sprinkle the potatoes with salt and pepper and then mop the potatoes with some of the chipotle lime honey mixture.
The potatoes cook for about an hour, so judge when to put them into the oven based on how long it will take for the chicken to cook. Place the potatoes on a baking sheet and bake for about 1 hour, basting with additional chipotle lime sauce occasionally. Potatoes should be crisp on the edges but tender inside.
When the chicken is done, carefully remove the beer can, tent the chicken with tin foil and let the bird rest for about 5-10 minutes. Carve the chicken and transfer to a platter. Arrange the potatoes on the platter and sprinkle with fresh cilantro leaves. Serve.