Breed doesn't so much matter as "prey drive". Prey drive is the instinct that causes dogs to chase. Some have very little, they could care less. Others have it to the point of it being an obsession.
Most herding dog breeds have prey drive. The trick is to train proper responce BEFORE an attack happens. Some dogs, once an attack happens, they just can't be untrained about this "fun" instinct driven behavior. Some can be trained to behave in your presense, others can be trusted fully... others are just hopeless.
I have 2 German Shepherds, one Working line bred dog who is full of prey drive. She desparetly wants to catch a coon or a squirrel. Anything that runs, really. If it's standing still, she doesn't care. She ran up on some baby squirrels, and they didn't flinch. She laid down, nose to nose with them, waiting on them to spring into action. They did not, they were either too young to seek escape, or knew to stand still was to survive. Who knows. I would trust her with chickens who were not afraid of her. But a running/flying chicken I would know she couldn't resist.
The other is an American bred Shepherd with little drive to do anything. Also male, so he's very lazy on top of having minimal drives. He would let chickens roost on him. He would watch them run, watch them fly, observant, but not really caring.
Same breed, different temperments.
I had a doberman who could not resist, knowing full well it was wrong to bother chickens. One made it into the back yard, she caught it and began to ever-so-carefully pull one tail feather out at a time. I went out the back door, she dropped the Roo and beelined it to the dog house, knowing the wrath she was about to see from me. Roo survived, only damage was missing feathers.
An Australian Cattle Dog (or Blue Heeler) I had would herd my chickens. She was very frustrated, since it's quite similair to herding cats. One false move and they scatter, and you have to start all over again. The chickens had no fear, and the Roos would even turn to fight her. She would drop to her front paws and bark at them, trying to get them back to the house in an orderly fashion.
Never once attempting to catch one, only trying her hardest to keep them together.
You'll want to start with a puppy, and spend a lot of timing teaching the proper way for it be around the chickens. And like anything with a puppy, don't set it up for failure by leaving it alone too early with the chickens, just like you wouldn't tempt fate by leaving all the shoes on the floor during teething.
When you go to choose a puppy, look for one with a calm, non-chalant demeanor. Not the one running around picking on the others, not the one "looking" for trouble or who's biting your nose when you hold it. You don't want the trouble maker, cute as they are, when the dog needs to be able to live up to certain expectations in it's future.
If you choose a border collie, start a "ball obsession" early. That way the dog only cares about the ball... not the chickens, not the gym shoes by the door, not digging in the yard. It's all about the ball, or the frisbee, or whatever toy the pup focuses on. Just be sure it isn't the chickens! Play fetch near the chickens, so that the conditioned responce is "chickens near means ball game... Yippee!" for example.
You just need to have a focus for the dog, regardless of breed, so that it doesn't focus on the chickens. The before mentioned Jack Russel for example, has chosen to protect the chickens, and it's focus is on anything that should show up to harm them. Other dogs mentioned ignore the chickens for fear of displeasing their human. Low-drive dogs are able to do this easily.
I had a Boston Terrier/Beagle mix that would let the baby ducks sleep on him and he liked it when they followed him around like he was momma duck. Very cute! But, a full blooded beagle stayed with me for a time, and she killed 5 call ducks and injured 2 Pekins in a 5 minute span when she managed to get in with them while I went to change laundry.
It's the individual dog, more so than breed, but choosing a breed without a strong prey drive is a good start.