This is what you need: http://www.rockler.com/findit.cfm?page=5263 It is a $94 unit that installs in your cabinet where a drawer was. It even includes simple hardware so that your existing drawer front is made to flip down so the cutting board can come out. Just have the contractor do the kitchen as planned. Just make sure there is a wide enough drawer where you want this thing to be, ie: at least 14 11/16" clear inside the drawer opening.
breadboards and breadboard channels: http://www.rockler.com/findit.cfm?page=2299