Despite Mahlkonig's warnings about the ProM not being user serviceable, you can open it up quite easily by removing the two tiny vertical screws that are just forward of the chute. When you do that (and remove the hopper), the entire top assembly, including the silver "Mahlkonig" face plate, will slide forward and off as a single unit.
The chute assembly is attached to the burr chamber (the yellow object in the diagram). The chute slides off after you loosen the little screw at its top (which I assume also acts as an anti-static ground). If Mahlkonig hasn't sent you a parts diagram, PM me, and I'll forward it to you.

I learned all this last night when I replaced the plastic chute, which had stopped removing static after a year. I'm a total non-DIYer, and it took me about 10 minutes. You will then have better access to the burr chamber. I didn't need to open the chamber myself, but it looked pretty easy to open up by removing a couple of screws.