Biodiesel is a pretty good lubricant. I imagine a few additives could give it the right viscosity and flow characteristics. Is that sort of what you're looking for as a chain lube?
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Plain mineral oil that you can buy at the drug store makes an excellent chain oil. I've been using it for years. It was recommended as an environment-friendly alternative to the ol' red stuff.
It's also been used in edible-mushroom cultivation experiments: basically, they mixed spores in with the mineral oil for the chain saw, then made their cuts to seed the logs. Reportedly with good results.