Sorry but, unfortunately, I don't have a digicam and my 35mm wouldn't capture the details needed (it doesn't take great close ups).
Ok, picture the metal tube that the ball bearing sits in. Insert one prong (is that what it's called?) of small needle nose pliers into the tube and gently grip the tube. Then slowly bend the end out 'til it's flared a tiny bit. You may need to do it in more than one place on the tube but after each bend check to see what the water flow is like. The flare on the tube allows the water to run past the ball bearing instead of sitting in the tube. Basically what you're doing is damaging the tube so water will drip out. The trick is to have it come out slowly. 
Make sure the pliers are clean and like I said before be very careful not to have any sharp bits sticking up.
Good luck if you decide to try it and please let me know if it works for your cham!
Meemee
Oh, I almost forgot to tell you that I change the water regularly, I don't wait for the waterer to run out. I figure the water must get kind of stale after a while, not to mention the risk of bacterial growth as well.