Find a position with the longest sequence of unique losing moves, i.e. white to move has one and only one move that will lead to a lost (for white) position. White makes this move. Now black by definition has a winning position. But we require there to be one and only one move that will turn that into a loss for black. Etc.
Clarification: If you can give proof that no other move loses eventually that's great but probably quite difficult in practice, so "doesn't lose within ten moves" or so shall suffice.