Chain shouldn't tear up the gears, but if you have something other than a drive train (ie: something that will include a huge load on it - arm, or other such load) your gears could get their teeth torn up...
We made a gear box my first year in FIRST (2001) and by the end of the season, the welds we used to attach the gear to the shaft help up awesome... but left the teeth the weak point, & it resulted in a half-moon shape gear. (The application was just a gear on gear mesh without using any chain & we were lifting full size robots & the goal that year which was about 150 lbs as well, all while putting that gearbox to it's full potential, & obviously past it's limit.)
Would have worked great as a cam, but unfortunately that wasn't our intended application of course.
We have since learned quite a bit about drive trains, & gearboxes & don't have that problem any more. (knock on wood).