We would prefer you hang it as a show piece on the wall of your kitchen!  (a couple spot lights would be a nice touch) A more reasonable way to store your cutting board is on your countertop leaned against your backsplash or wall. This allows your board to fully air dry after each use which will prevent unwanted moisture that leads to bacteria growth.  You could also store it in a cabinet or pantry space, once it is completely dry, as long as you store it standing it on its edge.  Storing your cutting board laying down, in a flat position, could result in your board warping over time.