Apple has been a good choice for that, but I'm sure you can use just about any other kind. That being said, when I want some good smoke flavor, I've always cooked my chicken via "smoke-roasting" (high heat indirect) because it's been my experience that smoke imparts way too much on the meat and then can be quite bitter (if it's cooked at a lower temp, and on the grill longer).
After a bunch of delays, I finally got a chance to make the chicken yesterday. Thanks to the advice here, I used some apple chips, cooked indirect and then finished direct to crisp up the skin. To my great surprise, the family devoured the bird.
If you like jerk flavors but are worried about too much heat, I highly recommend Penzey's jerk seasoning. My kids even enjoyed it. Personally, I like a little more heat, but it was perfect for the rest of my family's tastes.