These can be tricky to pull off on charcoal, but, as Steve Raichlen aptly observed, "No guts, no glory!" If you pull it off, you're in for a wonderful meal. The main challenge is that you need the fire to last for about 40 minutes. To do this, you get a chimney of charcoal going, dump it into your grill when it's ready, then add a whole pile more charcoal and wait a little while until the whole mess is ready for grilling. It should look like this by the end:
As I've mentioned before, beer is actually a piece of safety equipment when working with live fire. Since it's always in your hand, you can use it to douse flare-ups, and keep your mesquite smoking rather than burning. (Only problem is that it takes two of these 500ml puppies to finish cooking, THEN you have to eat!). In front of the beer are the chunks of mesquite that you put in the grill before you put the grate on. No need to soak the wood, but you should keep it as far from the charcoal as possible (trust me -- it will get hot enough to smoke -- it will also ignite now and then, but luckily you will have a beer in hand to douse the flame.)
Check the temp. Not strictly necessary if you are eating alone, but if you have kids, or guests who will sue you, best to check. Plus it sucks to sit down and then have to go back to the grill to fininsh the job. Chicken is sterile at 170 C.
Grill some asparagus while the chicken is finishing, plate up with some Chimichurri, and prepare yourself for a life altering experience! (Sorry for the fuzzy picture -- must be the beer.)