I experimented with this just to see what would happen. The chiller lowered the pressure too much, causing the skimmer to barely skim.

Even if it did skim, I dont think it would have been a good idea to put too much back pressure on the chiller tank seals. Thanks Ace.

Jose, I do have a manifold device on my main pump. I am going to experiment and install another T fitting to supply the chiller.