Check your credit card terms of service carefully. Cards do have consumer protection, but generally it isn't about this type of situation. If you owe the fee then it is fraud to do a chargeback and you can get into legal trouble (though odds are as the other poster said: they will just send you to collections and it will hit your credit report).

I agree that this type of change to contract terms is not acceptable, but unfortunately you need a lawyer to fight it.