Dirt works just fine, they will burrow around and dust bathe in it all day.
I've also heard of people using various things on the floor for the chickens to scratch in. I've personally used coastal hay and it was fine, but I've heard of people having problems with their chickens eating it and getting a crop impaction. Also, if it gets rained on a lot it could mold which is bad for them.
My experience with the hay was that it was cheap to cover a large area and that it looked nice. Also, the chickens had a blast scratching around in it for the bugs that would hide underneath. The downside was that I eventually had to rake all of that hay up and remove it for composting once it was dirty. Not so fun.
I've heard of people using dead leaves as a floor covering, and this sounds like it would work better because it would give them hours of fun while they scratch through for bugs and they will shred the leaves down and compost them into the dirt so you wouldn't have to shovel them out later. Now, the only issue, I guess would be finding a place to get enough leaves to fill your run.
My current run just has the dirt floor, and they seem to be just fine with it, though they prefer to free-range whenever possible.