Rather than build a permanent chisel rack for my tool cabinet, I wanted one that would double as a holder when taking woodworking classes or giving demos. So, I built this chisel holder based on one I saw in a ww book which had feet that would keep it stable on a benchtop. Then I built a little shelf with a lip and installed it in my tool cabinet door. A simple turnbutton keeps the holder from tipping forward.
In order to keep the chisels standing upright rather than banging into the walls of the dividers, I glued foam inside each cavity. Upon completion and having placed all the chisels in their respective slots, I realized an unfortunate design flaw. Sitting on a benchtop, it's a little unnerving staring down at all those razor edges pointing up at you. Hence, the chisel booties.
If you decide to build your own portable holder, you might consider shortening the height of the front piece to allow for an open section at the bottom. That way you can point the business end downward and still see which chisel is in each compartment.
Another thing—I cut all of the dividers an 1/8" short and only glued the top half in the dadoes. That way, the dividers are always flush with the top of the holder and can still move with the seasons.