We have two dogs that have accepted they are on the bottom rug of the pecking order with the chickens.
I really thought there would be problems with our German Short hair (bird dog), obsessive chaser of squirrels, rabbits and other small animals, (except cats- cat are above her on the pecking order too). But I made sure I was supervising her when she was young around the chickens. (okay, she also wears a shock collar, which made it easier). I don't even want her snooping in their coup when they are out roaming. I started off letting the chickens outside the last couple hours in the day and spent the time in the yard, observing. I shocked her one time when she decided to enter the coup and never had a problem since. Now she's actually afraid of the chickens.
Our Cattle dog, we got at the age o 2, was a little trickier. He first started rounding them up, and of course the chickens started to squawk and flutter about, exciting him. He needed to be disciplined several times for showing a bit too much interest in them. I really didn't trust him for about a month around my layers. We also broke his natural instinct for trying to herd our cattle. Our cattle are not chased and herded, their led, usually with food involved.
Now both dogs act like the chickens don't even exist and get out of the area when they are approached by them. Kind of funny seeing the chickens chase the dogs out of their area.
I think they certainly can coexist but they need constant supervision in the beginning. My biggest problem is I sometimes forget my chickens are out and friends or family come over with their dogs. If I remember I just don't let them out in the evenings or try and herd them up into the coup.