Domestic house cats very rarely attack adult chickens, but they can be a serious danger to baby chicks, and occasionally to juvenile birds or small bantams. That said, not all are, to be sure.
With chicks, it's better safe than sorry, but there are plenty of examples on the interwebs of cats cuddling and loving on baby chicks, like the above.
Occasionally we do hear from people whose cats seem interested in their adult birds. Since many of the most common chickens are just as big as house cats, this is pretty rare. If a cat kills an adult chicken it would be something of a struggle, and the chicken is just as likely to do damage to the cat as the cat is to the chicken!
Cats are carnivores, sure, but their preferred prey are very small birds, rodents, small rabbits and so on, not your eight pound hen!
When a cat kills a chick, if it is in the brooder, it may kill or hurt several at once just from having trod on them in an enclosed location... and if that cat is yours, she may actually bring you one or two as a "gift." Not fun! However, feral cats who get access to your chicks in the yard may eat what they have killed, often starting with the head.
Having cats around adult birds is a good thing in most cases: cats will hunt and kill any mice that are attracted to fallen feed, thereby helping to keep away other predators like snakes or weasels that may be attracted to the same prey. Just be sure to keep your baby chicks and smallest birds secure.
Protecting Your Flock
To keep your baby chicks safe from house cats, simply keep your chicks in a secure brooder. A cat will stick her paw into a brooder and try to snag and pull out your babies, so use a secure screen or fine mesh hardware cloth. Make sure your cat can't overturn your brooder, either, or lift the lid and nose in! Cats may want to jump on top to investigate, so make sure your brooder and heat lamp are very securely seated. We suggest you keep your chicks in their brooder away from your cats entirely, perhaps in another room.
For adult birds, again, cats will very, very rarely be a problem. However, if you do have a cat that will actually stalk and try to kill your adult birds, you can keep your flock safe by providing the same protections you would for protecting your flock from bobcats or lynx. Please see that entry for more information.