Can't use cedar, or cypress, have to stick to hardwood or pine. The best way is to call around to tree trimmers, and ask for a dump when they're close by, supposing they know what trees are chipped into the back of that truck. Untreated, all natural, straight off a tree. Typically, free on top of it. A lot of them have to pay for a place to dump. They'll dump it in your driveway for free and save themselves some money. Some won't do it because they use it or sell it. My mom used to flag them down at red lights near our house, when they just happened to pull up. I'm guessing a phone book could be just as effective. Usually some leaves and small twigs and things will be mixed in. But you can't beat free.
The only thing about mulch and chickens, is poo build up, moisture, and the subsequent odor from that. Add in warm temperatures, and you can also get white fungus and some mold. So you only want to give them small bits at a time, just a corner to play in. Covering the whole floor of the run several inches thick will breed additional issues in a moisture driven environment.
It will look really pretty on day one, and the chicks will get a lot of fun on it. What sucks is when you notice an issue and you have to shovel it all back out. Leaves are way better for entertainment, the chicks nails' tear it, and it breaks down much faster.
