The diagram above shows what's going on when your braking with the front brake.
1) The brake cable comes under tension
2) The brake pads apply braking force to the rim
3) The ground applies backwards force to the tire
4) The fork deflects backwards
5) Fork deflection causes brake cable tension to increase
6) Brake pads apply more force to the rim
At this point, something has to give way:
a) The brake pads stop the wheel cold and you go over the handlebars
b) The ground gives way and you have a front wheel skid
c) The brake pads slip on the rim and the vicious cycle of (1 to 6 + c) repeats
The rapid repetition of that cycle is 'chatter'.
How do you solve it?
- Decrease free brake cable length by mounting the hanger on the fork (like older front suspension mountain bikes: http://www.sheldonbrown.com/harris/images/tektro1257.jpg
- Install linear pull brakes which don't promote this behavior: http://nippleworks.blogspot.com/2008/12/linear-pull-brakes-with-drop-bar-levers.html
- Monkey with toe-in and otherwise change the mechanical advantage of the brakes to minimize the effect
- Install a really compliant cable hanger to deflect under cable tension?
- Disc brakes?