+1. I'd dig a shallow trench to make things level. I don't have a predator apron on my chicken run, but I do lock up my birds every night in a Fort Knox coop. If you have concern about animals that might try to dig into the run, than a predator apron would be a option to consider now before you put down your coop and run.
Depending on the slop of the ground, you might be able to use that to your advantage in that rain water will run off instead of pooling up in the run. Digging a shallow trench for the frame of the coop/run would leave your natural slope for better water run off. The chickens won't care if the chicken run ground is level or not.
Also, you will probably find that the chickens will eat all that beautiful backyard grass down to the dirt in a matter of a few months. At that point, I turned my once grassy but now dirt chicken run into a composting system. I bag up my grass clippings and dump them in my run, along with leaves, wood chips, etc... The chickens will naturally mix and level everything in the run. It makes great compost after some time.
If you want to keep some natural grass in your chicken run, I think now would be the time to build some 2X4 grazing frames and plop them down on a patch of your grass inside the run. That will protect your natural grass inside the run from being pulled out by the roots and will still allow the grass tips to be eaten by the chickens. When I expanded my chicken run into a fresh grassy area, that is what I did and it works great. I still have fresh growing green grass under the frames while the chickens have ripped up and destroyed everything else in the run.
Looks like you have bought a nice setup. Please post some pictures of your coop and run when you finish your build.