batman - call it a silly idea, but what about a drive belt that fastens to a chain? The chain is embedded inside the belt, and can only be connected once. When the flappy bits on the belt are closed up around the chain joint, chain is invisible.
Advantages are a sealed chain with no teeth will last much longer than a regular chain rubbing on teeth, and that its completely sealed so lubed for life of the belt.
Downsides, its not going to be as flexible as a plain belt, or as light.
Rust might be an issue if the belt absorbs water and holds it.