I've used the chainrings/cogs and chain off of various cheap bikes in the drivetrain of a scooter powered by a gasoline chainsaw engine. I'm not sure how much power the chainsaw engine puts out, i'd guess about 2hp. I used a jackshaft arrangement to reduce the RPM, and it drove a 12" wheel quite well. It would hit close to 30 mph on the flats, which was quite enough for me. Never broke a chain or anything.

Assuming proper chain tension, I think the problem would be torque. The parts can handle high rotational speeds but they're not designed for a whole lot of torque.

What are you building?