Today, as I was walking from the yard to the porch---I felt so much COOLER...and now I know why the chickens are always trying to come on the porch when they free range. They are actually pretty smart.
It made me think that I could get some sort of large 'play pen' with water food, Newspaper? -- both for thier reading enjoyment and their poo protection--and they could be cooler--but not fully at liberty.
There are a number of constructions made from PVC pipe and bird netting or chicken wire designed to contain the chickens. Instead of doing a lot of chasing, maybe you could do some enclosing and they could gain the coolness they are seeking. (guessing here that your patio is shaded and your weather is hot like ours is)