I don't understand what they are doing now as far as chicken lines, and we never used one, but back when we were sailing Hobies, I thought it was just a sort of slack rope from the front beam to the aft beam, and when you were out on the trapeze, you held onto that rope so you wouldn't go flying forward if the boat nosedived. I don't know if it was kept more taut somehow (when you weren't using it) with bungee cord somewhere or what. Like I said, we never used one. But the basic idea is to have a rope attached to the front and back of the boat that you can hold onto to keep from flying forward, or to help hold you to the boat while you are trapezing.

Anyway, that is the general idea and purpose, no matter how it is set up.