I would try solder first, but I doubt it will hold. Better to find someone who will spot-weld it. Should be cheap.
I actually called my local tech today to ask him about soldering it, and his suggestion was to get some super glue down in the gap between the key and the post. That sounds promising to me, so I might give that a shot first. He's seen this happen before, and he said that the solder often doesn't bond to the chromey plating very well.
To clarify, the key doesn't feel like it will come off right now -- it just rattles back & forth in the slot in the post. So I think the super glue might be enough to stop that.


