We have chickens, bee hives a cat and now a four-month-old Anatolian puppy that we have had for about a month now. We keep him as an in-house dog though he does get yard time with the chickens and our neighborhood squirrels. Ditto prior poster who said that this is a dog that you definitely want to get as a puppy - they're stubborn, prone to independent thinking and while they can be trained they will never be obedience heroes. Getting them young will help in the training department, not that the dog will listen to you if it perceives a threat. They're recall is terrible from what I understand.
That being said, we have (so far) been having a fabulous experience with our puppy. While he can be stubborn he has mastered basic commands and (usually) obeys. He's proven excellent on a leash after less than a week though he's prone to stop and survey if there are unfamiliar people in the neighborhood - the guarding instinct is strong and there's really nothing to do except respect the dog's desire to protect. I'm hoping that as he gets older he'll develop the confidence the breed is known for and stop less. They are highly intelligent dogs and ours had a pretty good handle on basic commands after only a couple days of training for each new command. Puppies chew a lot and they are no exception. Problem is, if Malinois and German Shepherds are the bullsharks of the dog world that will usually maim then the Anatolian is the great white that kills with one strike; by the time you see your puppy take its first bite out of your favorite pair of shoes it's already too late. They're bite pattern is huge and demolishes everything. We've mostly avoided this with lots of chew toys. Lots and lots and lots of chew toys.
Pros: quick to learn, mostly sedate (though a couple times a day he will get playful), affectionate to us and our neighbors, non-aggressive to the chickens (though he freaks them out just by walking near them due to his size), gets along with other dogs and our cat, is a dear at the vet's office (he slept through all his vaccinations) and is overall a sweet dog, although this is probably owing to the intense socialization we've subjected him to.
Cons: They're huge. Like, really, really intimidatingly huge. Our puppy's sire and **** were taller than if they put their paws on my shoulders and I'm six feet. At four months our dog is already over 40 pounds. If you don't get a puppy that you can socialize during that formative pre-14-week age I would not bother with this breed (a proper introduction to chickens is critical). Same goes for training - sure, they're not obedience heroes but you can bring them to heel with some work and this breed is just too freaking big for an owner who doesn't successfully establish dominance and properly socialize them to avoid aggression. Also, they're fairly impervious to pain, which is probably not great. Ours has managed to stick his nose into the beehives a couple of times and has been stung multiple times on his face and muzzle only to shake it off and do it again moments later.
There's a national Anatolian organization that has a terrific guide on properly training these dogs as there are some practices used with other breeds that are not appropriate to these dogs.