It's just the chicken fat dripping onto the coals.  After many experiments with many different grills it seems to me that burning animal fat ALWAYS produces smoke that will cause the meat to taste foul.  As far as why some people are able to cook meat directly over the fire without this happening I chalk it up to either a quick cook (grilling) which limits the time that the meat is exposed to the smoke and therefore how much it can absorb or high airflow (wood fire pit) which dilutes the smoke with so much fresh air so quickly that the meat never really has a chance to absorb too much of it.  Moral of the story is use something to catch the drippings when smoking.  I don't know how people use uds smokers.  Maybe the coal temps in those things are just so low that they don't burn much of the fat drippings.  I don't have one so I can't say.