Is it safe to use a cast iron skillet over a chimney starter? I want to pan-fry a burger tonight, but I don't want the smoke or smell in the house (we don't have a range hood, just an anemic exhaust fan that dates from the Truman administration).  I considered grilling, but I don't want the trouble of cleaning up the grill.

So, in true mashup form, I figured I could combine the two and heat the cast iron skillet outside on top of my chimney starter.

Is this okay?  I've seen people sear tuna above a chimney starter, but I haven't heard of using it like a campfire.  

Cooking-wise, I don't care too much about having the heat concentrated in the middle of the pan - I'm more concerned about unwittingly damaging the seasoning on the pan or something.
I don't think you will hurt the pan, cast iron skillets can take a lot of heat. I think the biggest risk is that you are building a kind of dangerous tower. If you were to somehow knock it over you could hurt yourself badly.