The CFC sits on the ice chest because where the dark green hose meets the metal, it drips a bit. It's only water though, from my sink.
The beer flows inside 10ft of spiraled copper pipe in the bucket of ice and water.
Brew kettle>>>>counterflow chiller>>>>copper pipe in ice water>>>>primary
Counterflow chillers are nice, I must say. I like having the beer not be exposed to the air like it would be with an immersion chiller. I know people do it all the time with no contamination, but that's just my research carrying over into my brewing (I work with tuberculosis bacteria). Plus it gets better efficiency than an immersion chiller.
Only problem with both immersion and CFC's is that unless it's the dead of winter or you live far up north, your tap water's not going to be cold enough to get the beer to temp by itself. Hence why I have the copper pipe and ice bucket.
Pumping ice water through your IC would solve that problem too.