You have opened up a Pandora's box Littlestrike. This is a very sore point for me also. Dear sitesurf has explained this to me a few times and I still dont really get it. The topic is "Dropped Articles" and sometimes it is Les and others it is Des. One, or both of your examples could give rise to a dropped article in translation to English and there must be some sort of guide. Maybe it is one of those bizarre things we just have to memorize AGAIN!
MIchellePK, a better translation for "I want to eat THE chicken." is "Je veut manger LE poulet."
One of the reasons for the use of "du" in this sentence "Je veut manger du poulet." could be the speaker/writer isn't specifying any specific chicken, but some chicken or chicken in general.