Ferd's method works, assuming you can actually manage to help with the dishes (the trick to that is to just start doing it, rather than ask... if you ask, the host is obligated to say "no, of course not," since it is understood that you don't actually want to help with the dishes), but the one I had in mind is you take a serving implement, pick up the last piece of chicken, catch the eye of someone else at the table, and offer it to them. They, of course, are obligated to say "No, you take it" (as are you, if someone offers it to you). If you are a guest, or the youngest person at the table, it's OK to accept at that point. Otherwise, you can look around to the table -- with the chicken still on the serving implement in your hand -- and ask if anyone else wants it. They all say "no," of course. Then you can serve yourself.

Which was all way too complicated to explain to someone who was having trouble with the idea that "Oh, can I have the last piece?" was rude by local standards.