Specifically, I dreamed of a chess variant where the board consisted of sixteen numbered pieces like the little graphic to the right. They're laid out four by four to make a standard chess board and the game plays out pretty much like regular chess. The big difference is that at the end of each black move 2d20 are thrown. The numbers rolled indicate which two sub-boards to swap in the array, transporting all the pieces on each.
No details in the dream indicated what to do when you rolled more than a 16 on either die, or how to resolve transporting a king into check. Obviously you could roll a d16 to eliminate the former problem, but maybe a roll of 17 or better indicates that you should skip swapping boards. Maybe if the king finds itself in check the player could be allowed to rotate the sub-board 90 or 180 degrees to move him out of check, otherwise skip the swap as if you rolled a 17+. Castling, the pawn's double move and en passant capture would probably all need to be scrapped in this variant. Would a pawn that magically appeared in the last rank suddenly get a promotion? That would certainly make things wild and wooly.
Being able to respond to white without the boards mutating seems like a tremendous advantage to black.
I don't recall every reading of a game exactly like this on the Chess Variants Pages, but it wouldn't surprise me to discover that it already exists.