If you get a young puppy and raise it with the birds, you'll have a better shot. I know many people that have chickens and dogs that have no problems. Or you could simply keep the chickens in a coop & run rather than letting them wander around at will.
As other have said, it depends on the dog. I think a small dog would be a better bet than a large one. My mom's pugs visit my house and are pretty good with the chickens. But definitely avoid labs, retrievers, and other hunting dogs.