I've seen this before. it was basically an automotive timing belt wrapped around two custom made pulleys.
Belt drive is common on motor cycles but it's not so hot on bikes for a few reasons.

1. cant shift
2. since they are wider, needs bigger clearances around the stays and crank (CUSTOM).
3. i believe they wear faster

Steel really is the best thing for bike chains because it is very strong compared to anything else besides carbon or exotic $$$ alloys. But, carbon doesn't have the wear resistance of steel, so it would wear out faster on top of being incredibly expensive.

nickel plate and plenty of lube is the answer.