Chattering is a real bugger. It's a bike racer's nemesis!
Most of the answers given already are right, but if it was as simple as that then you wouldn't hear MotoGP riders complaining of it.
I could reduce front end chatter on my CR250 retard by changing the spokey dokey wheel to a (heavier) NSR wheel. Similar thing to what Steve says. This heavier hoop decreased the speed that the front wheel moved through the suspension stroke, so chatter wasn't as violent.
In your case I'd increase the rebound damping on the front. Sounds as if it's starting to lose traction into the turn, and as it does it fires the front wheel away because of lack of damping, than grips then slips etc, and so the suspension loses control.
How does it feel on the anchors? A bit squidgy? In the case of the NSR, the stock forks ain't much cop as they're built for a 55kg Jap to cruise Ueno at 3am making a racket.