How do I get a burnt-on plastic bag off my Rowenta iron?

I accidentally left a plastic bag near my iron and it burnt onto the plate. It is a Rowenta iron, it has a very shiny plate. The plastic is hard as a rock now,
I have tried to chip away at it but it is not coming off and I don't want to scratch the surface of the plate.
I called Rowenta and they offered no help at all. Said they had never heard of this problem. Surely someone out there has experienced this??!!!!! Any suggestions are appreciated.