There is no rule that causes you to loose points, but if your robot becomes an entanglement hazard during the match you will be disabled and asked to fix the problem before your next match.
As for chicken wire please follow the acceptable use flowchart and if you want an official ruling on it please have your team Q&A representative post it on the official FIRST Q&A system.
http://usfirst.org/robotics/2006/qa.htm
In my own opinion i think it would be allowed but i still recommend asking in the Q&A forum