Hi Mac,
Depends on how you look at it. From an organic raising perspective, it's not okay to use pressure treated anywhere, including the run. You would think that perhaps the toxic effects would be a bit less in the open air of the run than compared to the closed coop. However, if they're ever going to be scratching in the soil near the pressure treated timbers, then they would be exposed to its toxins that have leached into the soil (not to mention if they ever peck at the wood itself).
Other options to consider would be redwood or metal. Obviously, redwood would have to be replaced more often, but it may be the better option if you don't have the tools to cut the metal. I personally prefer the aesthetics of redwood to metal as well, so that's what we'll be using for our coop and run.
And to retard any decay on corner posts, you might consider pouring a concrete mini-caison and attaching the redwood post to it with one of those metal brackets that suspends the post above the caison a few inches. Sorry, don't know all the technical lingo here (that's dh's dept), so if that doesn't make sense, post back and I'll have him explain it.
