This is something I am worried about too. I have two dogs, one that has grown up with cats but still likes to chase them. He doesn't hurt them, but wants to play with them. But, he is a 90 lb pit bull mix and will hurt them just by playing with them. My other dog was a forest dog that adopted us when we moved here. She lived in the woods behind our house. She is a border collie mix and lives to chase and catch squirrels. She has learned to leave the cat alone, but if I am not looking she will give chase. Her goal in life is to eat one of these new babies.
I have my new babies in a dog house converted brooder. The front door opening is permanently screened shut with hardware cloth. Both dogs will lay there and watch the babies. They will start to cry and if a chick gets close to the door they will paw at it or bark. I was hoping to get to the point where they could be with the chicks without hurting them but I don't see that happening anytime soon.