Someone mentioned Border Collies. One of the worst offenders Ive had is this breed.
A natural herder, thanks to centuries of development, BC's have a highly developed drive. If they don't kill the birds outright, they drive them near to death by rushing and trying to sport with them.
That is the real worry - sporting. The domestic family dog isn't generally trying to kill the chicken for food. That is common with feral dogs; not so much with Full-Belly Fido. But the subverted prey drive which all domestic dogs possess - that which would have them attack a chicken - has been morphed into a "sporting" instinct.
The dog simply enjoys the squawking, flapping, neurotic ball of feathers that is The Chicken. I can relate to that.. I enjoy chickens, too.
But dogs have weapons: Speed and utter desire, sharp fangs and claws. Yet, sadly, they lack the judgment you and I possess. They are helpless victims of their own appetites.
I've had three flocks of chickens utterly destroyed by my own domestic hounds. In each case, not a single chicken was eaten, mauled or even much disturbed. They were all, however, throttled by the neck until dead.
The dogs will chase them, utterly caught up in the event once it begins. Feathers fly and chickens run, squawking for all they're worth, with the dog hot on their tails - until they are captured and attacked at the NECK. The dog, out of his mind by then with feathers, adrenaline and exertion bites down hard and does the "head shake rattle" - you know, the same one the one they do with your old socks. Well, chickens succumb pretty quick to that. Begaaaaawk!.............
Once the bird becomes lifeless - the dog goes on to the next one until all the birds lay dead, in a heap. It looks like a battlefield. Unlike some other predators, the dog will often kill as many birds as he may find, until they are dead or the dog is stopped. Its one of the hallmark signs of the dog attack - dead chickens all over the place.
Im certain my dogs still fondly remember those times when their masters chickens (MINE!) provided them with so much entertainment.
Im pretty certain that big, lunking breeds and many traditional working types offer your best chance at a low-risk chicken dog.
Even so, the individual dog still needs to be taught that chickens are off limits. This is one of those times when an ounce of prevention beats a pound of cure.
Where you are dealing with a pack of dogs as I have, well... I'm not sure what will change that dynamic.