My chicken coop has two little chicken hatches on two sides which gives me the ability to have two separate chicken runs. Over time by using both chicken runs the area around the coop gets grazed fairly evenly. Sometimes when it hasn't rained for awhile the runs get overgrazed so I will give that patch a rest for awhile. The areas right under the two doors are always going to be a problem, but I do have an idea for that at some point. I've also worked out, that for us, narrow runs work best and prevent the hawks from swooping in and attacking the chickens.
The first photo is from this morning after I moved the fencing over about four feet to the right. You can see how well the chickens have grazed the run to the left. The rest of the photos are from previous moves this winter.