Rewiring an old iron, to what may I safely and effectively attach the ground wire?

I have an old clothes iron for which the original wiring did not include a ground plug. The new wiring does include one, but I don't know if I can attach it to the metal part of the iron that heats up or if this will cause problems by breaking the circuit between positive and negative poles. I don't see any metal parts that are not part of the circuit. I prefer to ground the iron rather than removing the ground wire.