Rolls with grass/ lawn contain lots of poison . This is not a good idea , certainly not in combination with chickens.Don't know if anyone mentioned this but we had the same problem, especially the most common path to drive to the barn it's just grass but thin and compacted.
We bought a couple of rolls of rolled excelsior.
https://www.siteone.com/en/landscape-supply-erosion-control/c/sh1213101100
It worked well and wasn't too expensive. Another year we scattered some of our hay over the seed and dealt with the weeds or volunteers after the grass was established.