Have you gotten in a disagreement with your neighbor or is this just a random act of inconsideration? If you have an ok or even cordial relationship, why don't you see if you can treat both sides of the fence so that it isn't ugly on your side? To me, even if they stucko over chicken wire, that sounds a bit odd- maybe see if you can contribute the extra money to have both sides look acceptable?

I know that "spite fences" are illegal in a lot of states. I think that you ahve to be able to prove that it serves no function though, other than being designed to be a nuissance to you