Depending on the size of your run, you may just want to put coarse sand down (if the run is not huge). It's good for drainage and easy to clean, plus it doesn't become a mudbath like some runs. Rock/mulch companies sell it pretty cheaply by the ton.
Of course if your run is pretty big, then I think a sand box (or kiddie pool) sounds like a good idea, for when your chicks are older of course. Unless it would be under cover, I would drill some little holes in the bottom. But sand generally dries out pretty quickly anyhow. Not when they're tiny, but when my girls got older (and I'll do the same with my new chicks), I would mix about a cup of food grade DE into their sand box, and even into the dirt in the areas where they liked to dirt bathe while free ranging...this was outdoors, so plenty of ventilation obviously.
Of course if your run is pretty big, then I think a sand box (or kiddie pool) sounds like a good idea, for when your chicks are older of course. Unless it would be under cover, I would drill some little holes in the bottom. But sand generally dries out pretty quickly anyhow. Not when they're tiny, but when my girls got older (and I'll do the same with my new chicks), I would mix about a cup of food grade DE into their sand box, and even into the dirt in the areas where they liked to dirt bathe while free ranging...this was outdoors, so plenty of ventilation obviously.