Can't identify these Thonet / Madison molded plastic dining chairs.  

I owned one once, several years ago, which I bought at a 2nd hand shop in Western Oregon, and similarly found it impossible to find another example of one anywhere. I believe yours is the only other one I have seen. Mine was also black.

This chair is similar in concept to the German Thonet design from the early 1970s called the 2100 Flex range by Gerd Lange. The concept was to have interchangeable parts made up of the wood legs, a plastic formed seat (some upholstered) and optional arms. It was intended for the contract market and they stack when stored and linked together when used in tandem.
I don't know much about how Thonet USA was linked to its parent German company during the 1970s if the same seating concept was offered in the USA, I do know that the Gerd Lange version was sold in the US too. Thonet USA eventually split with its parent company in the late 1980s when it was acquired by an American contract furniture company owned by Shelby Williams.
Have you tried contacting the current Thonet USA maybe they could give you some more design background on this particular chair?
Also, even though the concept worked initially and the chair was sold in large numbers, I had seen many examples of the Gerd Lange chairs in the past with broken unrepairable plastic seat parts but no available replacement (possibly from being discontinued?) and most likely just ended up in the landfills.