Nelson,
Since you are facing, rather than turning diameter, the three-jaw should work fine. The gear is 24-tooth, so that is divisible by 3, meaning that the jaws can be set on gear crests. I would suggest slipping a piece of pop-can aluminum between the gear and the jaws. Actually, the aluminum may not be needed for plastic gears, but I'll leave that reference in for those doing a similar operation on metal gears.
The trick is going to be in getting the gear to sit parallel to the face of the chuck. What I would try is to set the gear up with a bit more than the amount you want to remove sticking out past the jaws. Tighten it only enough to hold the gear and aluminum in place. Fasten a stick of hardwood in your toolholder and run it gently up to the face of the gear. with the lathe turning slowly, advance the carriage just enough to push any high spots on the gear into alignment with the low spots. When the stick is rubbing lightly all the way around the face of the gear, back it off and shut down. If the gear is still sticking out far enough to take off what you need to, tighten up the chuck to hold it firmly. If it got pushed in too far, move it out and try again.