I consider chickens very bright when it comes to direct associative learning. My experience is that they typically only need three or four repetitions to learn, as long as what they're learning is something they consider highly desirable or of real benefit to themselves.
If you have a big property and a fair bunch of birds who are allowed out to forage, you can try a simple experiment to observe this for yourself. Go to a place where and when you normally wouldn't interact with your flock, call them using a distinct phrase or sound, and toss something that they REALLY love to eat. You might only attract the attention of a few individuals that first time, who happen to be nearby anyway, and that's fine for the first go. Next day, do the same thing, at the same place and at the same time. You'll likely get more takers this time and birds that come running in from a distance when you call will attract the attention of others who will run up to get their share in turn. By the third day, don't be surprised if you've already got most of the flock waiting for you at their new favourite feeding spot when you go out. Not only do chickens learn that fast, but they also seem to have a great inherent sense of time. They always gather at just the RIGHT time if you're consistent about always treating and such at the same time every day...never too early and certainly not too late!
That said, it might surprise or perhaps depress you to know that insects can also learn via direct association and that they also typically learn after only three or four repetitions. I'm a bug fan and have taught lots of pet grasshoppers to climb willingly onto my hand as long as I then promptly transport them onto a fresh pile of yummy lawn grass. They'll also quickly approach and climb on a hand once they've learned that doing so will net them a tasty tropical fish flake. (Which they'll eat by holding the flake vertically between their two front feet while they nibble, like chipmunks...so cute!) So! I do believe that chickens are at least as 'smart' as grasshoppers or maybe it'll sound better to say that grasshoppers--some grasshoppers--are as smart as chickens. That's not saying much, most of you are probably thinking at this point, yet it's what I've observed for myself.
I'm not sure about the claims about how well chickens can count, though. My own experience with lots of broodies and their babies is that they're only capable of distinguishing between none, one, and more than one chick or chicks. If chicks fall behind and out of earshot, as long as the hen still has at least two chicks with her, they never seem to notice that others are missing, at least on a visual level. They've always responded very promptly to any distress peeping, though...if they can hear it, THAT they'll notice.
Compared to dogs, I feel that chickens, while very well served by their own methods of learning plus their keen ability to observe and their instincts, nonetheless lack the ability to form complex associations the way many dogs can. An example: I used to drag a long, long garden hose around with me when I watered all the critters in the summer sometimes, which included changing out the water in the bowls I placed in favoured hang-out spots for all to use. Most of the chickens, especially the bantam flock that favoured the front deck, quickly learned to associate my presence with fresh water coming out of the end of the hose and their bowl being refreshed. Put the hose end down on the deck and there'd always be at least one bird who couldn't wait and who'd run up to the hose and put their beak to the nozzle, expecting water, looking surprised when nothing immediately appeared. The same chickens wouldn't think to approach the hose, however, and expect water to appear if I wasn't present...it was me PLUS the hose that always got them going. And yet, on the other hand, I don't believe that they ever truly grasped that I was what activated the hose to produce that water. If their bowl on the deck ever went dry, I don't think it would have even occurred to them to approach me in an attempt to communicate that they wanted water and could I please come and give them some. Dogs, though, they CAN do this. I expect most people who've owned dogs have had one come up and let you know that they needed something, and sometimes what they need is for you to fill a dry water bowl! That's a practical example of the difference in intelligence between these particular two species, dog and chicken, which I've noted over the years, and I'm sure there are many other differences. And that's kind of the point, I'd say. Intellects vary. It's hard to say whether one animal is truly smarter than another sort of animal. I think it comes down more to how successful each species is in using what bundle of smarts they've been granted to survive and prosper, as it were. And chickens, you have to admit, have been pretty darn successful in the grand scheme of things...even if their lot in life for the most part is feeding other species.