Why didn't you start out with a wooden tube in the first place? They come in all forms and sizes as far as I know
Cut it in 12 inch pieces and drill a small hole through the center where you fix the chain, something like this:
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|----|
|----|
|----|
0----0 <------|| screw/nail (held by screw nut on other side)
|----|
|----|
|----|
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Run the chain all the way from first to last piece and keep it fixed with a screw that goes through and a screw nut on the other side. If it's only a prop it doesn't need to resist all that much force I assume? Just make sure the end pieces are properly connected.
Clear what I mean?
sorry for my lame ascii art
edit: you can also glue tubes of different diameter in between segments, to be able to just put it together.