Step 1: Remove the Fan Rotor
The first thing I did was to drill an exploratory hole in the hub of the rotor so that I could see what was inside and determine how it must have gone together. Since you are reading this, you can skip this part.
From looking inside, I could see that the motor assembly had been pressed into the fan. I drilled three more holes around the edge where I could see the metal ring that turned out to be the magnet. This allowed me to <u>gently</u> drive the motor out of the fan with a punch. If you choose to go this route, I recommend drilling the holes with just a drill bit and some persistence. If the bit is sharp it won't take long and you're less likely to slip and damage the guts of the thing.
Inspecting how the fan comes apart and goes back together, I am fairly certain that you could also take it apart with three small lever-type tools and help from a friend. Put the levers under the corners of the mounting bracket on the back of the motor and pop it out of there. Or, it might snap the tabs off. It takes a fair amount of force to remove the motor from the fan. Try it at your own risk. (I am reasonably certain that it will work though.)
I usually use white lithium grease for this kind of application since it provides good lubrication and is non-conductive, but feel free to experiment. Non-conductive is kind of a must since you really don't want your lubricant shorting out your motor, so stay away from graphite. Teflon wouldn't be a bad choice. Automotive bearing grease would likely work as well. The tiny bit of grease that remained in mine had the consistency and texture of a lithium-based grease, but there wasn't much of it, so I can't be certain.
Note that replacing the grease may or may not actually reduce the noise. If the fan was chattering when you took it out, the bearing has probably already sustained some damage. Packing it full of a heavy automotive bearing grease may well be your best bet. You can do that with a gob of grease and a toothpick.
It appears that the bearing is pressed into a brass hub, so it may be possible to remove it, but I do not have a bearing-puller that small. If you do, be aware it looks like there may be ball bearings inside, so be sure not to lose them.
When you are done, press the magnet back into the fan (assuming you removed it) and then press the motor firmly back down on the axle. It should snap into place and stay put. With luck you'll be able to squeeze a bit more life out of the thing until you can effect a more permanent solution.