It depends a LOT, I think, on whether you will lock the chickens into a secure shelter at night.
If you will, the run needs only to repel daytime predators, which with the addition of some sort of top (I might just crisscross outdoor-grade string over the top, to discourage hawks) it should be pretty acceptably safe. (I have a chainlink-panel run like yours, this is what I do when I use it, and it has been totally fine and dandy so far).
However if the chickens will *not* be locked away in a predator-proof little coop at night, I think that pen will cost you a lot of chickens or a lot of money or both. To really predator-proof it, it will need a STRONG roof (solid or mesh) - raccoons will go right thru chicken wire, I'd suggest either a solid roof (like, tin panels screwed to rafters and stringersm supported by 4x4 posts) or strong mesh such as 2x4 fencing that's bolstered in a few places with posts and possibly a 2x4 or two. Then your chainlink walls will need to be faced with something like 1" mesh or smaller, up to a height of 3' or so, to repel the grabby hands of raccoons (and it'll also helo discourage weasels and rats).
You may be surprised how fast the cost of all that adds up, so it may make as much sense just to build a predatorprood coop (house) and be done with it. If you do that (even if you could just adapt a secondhand shed or playhouse?), consider attaching it to the SIDE of the chainlink run (that is, adding the building in to the run's sides, so the run is no longer square) rather than putting it IN the run -- same cost, and your chickens will have a lot more room that way.
Hope this helps,
Pat