[SideburnsOfDoom]

>They are very interested in chess, despite the fact that they have eyes with properties that make it impossible to make out what actually happens on a chess board. (The whites and blacks and squares all blur together.)

I suspect that the real breakthrough would come when the alien physicist designs a very sensitive instrument that can observe exotic wavelengths of light at high resolution, and thereby show that the board is not uniform, but is divided into regions that have 1 of 2 states: i.e. black and white squares.