I'll put in another vote for Jeremy's suggestion of a drip edge. Especially if your roof is not highly pitched and you want your coop to last a good while without leaking or requiring fussing at. Cheap insurance against water soaking the edge of your plywood and rotting it.
I am particularly obsessing on the value of a proper drip edge *today*, because the gutters on the back of our garage came down in a wet snow a coupla days ago and I had to replace them yesterday *in the dark*. The already aggravating process was greatly complicated by it turned out that the idjits who did the roof (long before we moved here) did not use anything like that at all (not even a proper starter strip of shingles) and the fascia board and rafter tails are considerably rotting away, making it EXTRA jolly trying to attach new gutters, in, did I mention, THE DARK. Harrumph! Even if this is not going to be such an issue on your coop, it is a good reminder of what water trickling along the edge of the roof, instead of dripping freely away, can do.
Pat, who DID get the gutters up (with new drip-edge stuffed in there, too) but invented some new words along the way