I think its a bad idea to fix that part. Its not worth the risk you take when you use it. Its broken once under use and the probability is high it will break again. Its not a bad idea to repair the chuck but use another part. There are few things worse then seeing something flying across the room. You might want to consider replacing all the jaws.
Its looks like its something someone with a good milling machine could make.
Its looks like its something someone with a good milling machine could make.