Can a 10 speed front derailleur work with a 9 speed chain?

what? there is no such as a 9 speed chain OK, I don't know what this first "answer" was. To start from the beginning: there definitely IS such a thing as a 9-speed chain, just as there are 6-7 speed chains, 8 speed chains, and 10-speed chains. The difference is in the width of the chain: as the number of gears on the cluster goes up, the chain required gets narrower, as the space between gears gets smaller. Short answer: yes, a 10-speed front (or rear) derailleur will work with a 9 speed chain. The 10-speed front derailleur cage is very slightly narrower, so it may be a bit more fiddly in adjustment with the slightly wider 9-speed chain, but it is 100% interchangeable.