I recommend you start with a unicycle first.
Less than 1/2 the effort.
Nope. I can't ride a unicycle.
How long will it take to make a chain?
Probably forever, but if you consider that my challenge is to omit anything that was actually made for a bicycle - by a bicycle parts manufacturer such as Shimano, Sram, etc, then its possible to use an industrial belt or chain.
Will the frame be wood? Or are you going to roll&seam tubes?
Maybe I'll use aircraft tubing. Even EMT tubing would work. It would not be lightweight or double-butted, but it would work.
Assuming this is a fixie?
It might be. I'll have to wait to see how creative I can get on the lathe.
Remember, the 2nd man to invent the wheel was stealing intellectual property.
Waaaaay before my time to care! 
Final question: What, no bike co-ops nearby that could greatly use your time and skills? For a truly productive result.
The closest bike co-op is a hour away. They cater to homeless and other down-on-luck peoples. Those peoples only want Next bikes and other wally-junk. They have no desire to right a fine English 3-speed, and I have no desire to work on junk, so no. Besides that, I have my own bike shop to run.
Good luck with your project. A recumbent might be easier, if your chain making isn't too time consuming. Maybe front wheel drive?
I've given a lot of thought to building bikes for a living/hobby/pastime, but I'm getting long in the tooth for anything as serious as that now. Time to just enjoy the good things in life.
edit: searching revealed a follow-on project.
https://www.youtube.com/watch?v=zHtOcioXiQ8