[pdpi]

One move is 12 bits at most. 3 bits each X/Y, two XY pairs for source and destination.

[philsquared_]

You would only need one set of coordinates. The destination coordinates. Any high level chess players would only need that information to dominate.

[TakeBlaster16]

Honestly I think all you'd need is the piece. There are 6 pieces, so that's 3 bits of info with room to spare.