A friend of mine plays a chess variant he calls "Stress," a mixture of Stratego and Chess. I wanted to share the idea, but its a slight redesign and has probably been done before under a different name. Regardless, its an interesting compromise between double blind chess and simplicity. Anyway, I'm putting it under "General" for lack of a better place.
Each player gets 16 ping-pong balls glued to a checker piece with the name of the piece written so that only one player (the player who controls the piece) can see it. Pieces start in the orthodox order.
And that's it. Stress adds a simple layer of memory and later deductive reasoning to the game, but certainly players who are able to remember all of the pieces will play it no differently than any normal game of chess. However, for those of us who aren't geniuses there's a definite fog of war aspect to the game play that makes for a fun tension. Imagine my surprise when what I was sure was a pawn turned out to be, in fact, the queen.
So, a very simple variant, but perhaps applicable to designers looking for a double blind mechanic without three boards. Alternatively, pieces could be placed in a random order, or along the rules set out in Fischer Random Chess (pawns placed as usual, king placed somewhere between the rooks, and bishops placed on opposite colors). That would place more emphasis on the deductive reasoning side of the game.