Chickens love to scratch, turf looking for bugs, dustbathe & eat greens, so I've only been able to successfully grow grass because I provide:
* bare soft dirt, covered overhead, dustbowl area for baths
* a hardware covered area growing their fav greens, chickweed, etc.
* other things to do such as hanging veggies & flock block to peck at & perches to get shade & rest
We get a lot of rain here, but must water the grass during July & Aug drought periods, but I have to water my garden then too, so no big deal.
So overall...it works for me, for 3 yrs now. Prior to that I tried sand, straw, natural mulch, and muddy, slippery pens were a nasty mess & some chickens got bumblefoot. I tried grass one muddy autumn, thinking it'll be temporary, just so I wouldn't slip in mud, and it actually grew & has stayed decent.
I may have to fill in a few bare spots & apply some lime once a year in winter when we have a few days of nasty weather & my flock will be indoors anyway, like now, we have wind, snow, ice & rain for the next 3 days, so I sprinkled some lime last night.
The number of chickens, as well as breed tendencies, will also play a part. I have 5 Wyandottes in a 10x10 pen, they're easy on grass. I have 2 RIRs with 5 Marans in a 7x15 pen, very rough on the grass. I have 7 EEs in a 7x15 pen, they're not as rough as Marans, but still hard on grass. 5 Buff Orpingtons in a 10x10, grass stays nice. 20 sq ft or more per bird seems to be best.
Also, spring & summer I let them out to free range as I garden. This past summer my neighbor was feeding foxes so no free ranging, but the grass in the pens survived. This year I'm going to either fence in the whole yard or at least fence a grazing area so they can get out more, despite the foxes. The more time they are confined to a particular grassy area, the more they'll tear it up.