Personaly, I would just go out to your local Radio Shack and buy a new antenna wire. Did they chew through the wire or just the insulation on the wire. You could cut a section of wire from bothe sides of the damaged area and reconnect the two ends thus removing the damaged area, leaving you with one whole undamaged wire.
Yeah, its just like water pipes, if there is a crack or leak then you cut the section damaged out and then use new filler pipe with connectors to repair. In your case you probably just need to cut the section out and do some taping and your good.