Golly, I don't know the answer to this. But what qualifies as insoluble, for you? I think there must be some organic liquids in which chlorine is less soluble than it is in water. Would that be good enough for your purposes?
Chlorine is non-polat. It shouldn't be very soluble in a polar solvent like Acetone. I don't know whether they react together. Are you trying to do a separation? Added later. Chlorine does react with acetone. See http://digital.library.louisville.edu/cdm/ref/collection/etd/id/600 You are going to find it difficult to find something it doesn't react with.
From what I recall simple alkanes won't react without a catalyst and even things such as benzene may be OK. Acetone, sure, is asking for trouble with that carbonyl group just itching to do something…...: http://en.wikipedia.org/wiki/Ketone_halogenation
It's probably not necessary to say this, but I'll say it just in case. Whatever you are attempting, do it in very small quantities, and if you haven't got a fume cupboard, do it out of doors, upwind.
A candidate as carbon tetrachloride , I suppose it will not be soluble because of its density and there is no room for any substitution.
If you mix chlorine; Cl2 and sodium hydroxide (solution); NaOH, you will get sodium oxychloride; NaOCl, which is household bleach. This is a useful chlorine scrubbing strategy, because you can make a saleable product and not just another waste to dispose of.
Let me add to your comment . Take a concentrated salt NaCl solution then pass an electric current, you will produce bleach NaOCl and Cl2 gas.