The answer that came back from the echo chamber was "in your oven". But when you store these things in your oven you loose an oven rack. Or you have to heft this heavy thing in and out when you need the rack it sits on.
Finally, I've solved this problem. Actually I've been doing this for years, but have just now gotten around to writing it up for Instructables. I'll explain how to easily regain your oven rack . . . and why pizza stones suck.
* I feel the need to qualify the suck comment. Obviously from the picture my pizza stone is old and well used. Stones are much better than baking sheets . . . by miles. If your choice is to cook a pizza on a thin baking sheet or a thicker baking stone, then you'll be much happier with the stone.
Step 1: Needed Things
---Fire bricks (sometimes sold individually at home improvement stores)
---A heavy hammer
---A brick chisel (a tile/brick saw would also work well if you happen to have access to one)
Step 2: Whack It Up
Step 3: Install and Use
Return your racks to your oven and never worry about moving your pizza stone around again. You can leave it in your oven at all times, even when you're doing the self cleaning cycle (it'll actually clean your stone very well). You should be aware though that leaving the stone in at all times might lengthen the time it takes the oven to come to temperature, but it doesn't add that much time especially if you have a convection fan.
*Avoid galvanized metal as it might produce zinc fumes that are toxic.
Step 4: Why Stones Suck
The Baking Steel is a 1/4" thick (there is a 1/2" thick version too) slab of metal that will quickly conduct heat into your pizza crust. Fire up your oven to the top of it's heating range and let it warm up for 30 minutes and you'll get a very nice, crusty, charry toast on the bottom of your pizzas . . . much nicer than on a stone.
I first heard of the Baking Steel on seriouseats.com. Cooking pizzas on big slabs of steel are also talked about in the Modernist Cuisine books. You can see videos of the Modernist Cuisine folks using these steels on Chow.com. But this steel product isn't cheap. The only reason I have one is that I got it as a gift. If my desire for one had risen enough I most likely would have sought out a thick piece of steel. If you putter around the Stoughton Steel website you'll see that the guy that came up with this product used a scrap piece of A36 steel. So if you can find a good piece of steel, then make your own and save some bucks.