The lower end of your shafts will either need seals or to be covered if nothing connects to them. You could use a slinger to lift some oil off the bottom of the case. Imagine a rod or bar attached just inside the teeth of one sprocket. This extends radially toward the shaft, and also downward at a slight angle. When it is spinning, some oil will climb this rod due to centrifugal forces. Now imagine lots of such bars, or even a conical plate. That will get the chain oiled. To get the upper bearings will require more effort, and it may be best to rely on grease here.