We had this problem when we first got our chickens...didn't quite realise how destructive they were towards grass
Our chickens turned our lawn into packed dirt, which turned into a mudbath during autumn and winter. As a result they now live in a coop with a roof to keep it nice and dry, they are let out for maybe half an hour to an hour every day, and they get grass clippings every time we cut the lawn
Set up 2 runs...one on each side of the coop...rotate them in the runs monthly. It keeps them from getting bored too...
I free range mine...they are eating wild strawberries growing all in our lawn....next are the wild raspberries...they LOVE them. If you free range them and have the space to free range...your grass will be fine...mine actually keep it trimmed and last season I only had to mow 1 x in August!!
I cant really give them lots of room to run around, its only a 5m x 12m patch of grass. And even when i set up the run for half an hour or so a day in different places they still manage to dig loads of holes in the grass It drives my dad insane! He keeps threatening to fry them!
So far, five free range chickens on an acre of grass has been working out fine. We have no bare spots except the spot right in front of their coop. Lots of space per chicken does seem to be the way to go.