I too have gone through a few little chiefs, but have never had a fire. I use the box it came in to cover it (after cutting off one end and a couple of u-shaped cuts on two of the lower sides to clear the cord and pan handle). But the real trick, I believe, is to throw the pan that comes with the smoker away and get one that is deep enough to just clear the drip pan. The standard pan is too shallow. And I wouldn't put it up on anything that leaves a gap underneath. I use a chunk of thick particle board, but concrete surface is ideal, of course. The idea is to not allow enough air into or under the smoker to burst into flame. I use my own alder slabs for smoking, which are cut rounds about one inch thick. I use only dry wood and never soak it.
No air......no fire.