Prepare yourself for this: a chicken's vent is the opening where she expels waste AND the opening from which she lays her eggs. It's all one thing--eww, gross!
It's actually not quite as shocking as you might think. You can see here that the intestinal tract and the reproductive tract ARE separate things in your chicken.
They just end up venting from the same opening, the vent, which is under your chicken's tail. You can't quite see the vent in this photograph; it's just below the tail and just above the "fluff" (the soft feathers around her rear end).
"Cloaca" is the anatomical term for vent---and "wheezer" is the colloquial term.