After the chickens rip up all the grass, and you put down wood chips, you should be set.
If you are into gardening, then I suggest continuing to add as much organic material to the chicken run and turning it into a chicken run composting system. I bag all my grass clippings and toss them into the run. The chickens love to eat some fresh greens, and the rest gets composted along with the wood chips, leaves, etc... All my yard leaves get composted in the chicken run. Nothing leaves my property.
I use paper shreds as deep bedding in the chicken run, and the paper shreds compost down in less than 3 months out in the chicken run. Almost any organic coop bedding could be used to make compost.
The chickens love to scratch and peck in my chicken run compost because it is full of bugs and worms. They could not be happier. In return, they continually mix the chicken run compost and help it break down even faster.
I tell people I have composting chickens and gets eggs as a bonus. In fact, I "save" more money on the compost from the chicken run than we get from selling eggs. In the past, I used to buy big store compost at about $6.00 per bag. Now I harvest the equivalent of hundreds of dollars of compost every year from my chicken run that I use in my gardens to grow people food. It's a pretty good system.
A good chicken run setup should not smell. If you put down a good layer of wood chips or go all out and make a chicken run composting system with grass clipping, leaves, etc..., the run should smell like a forest floor.