We have five dogs - and our chickens are securely fenced. I think if you can't keep your animals safe together, you have to be responsible enough to keep them separated. How you do that depends on your situation, priorities, and point of view. My dogs get along fine with each other and with the cats, but I wouldn't trust any of them for a second with the chickens. Three would eat the chirps, the other two would try to play with them and/or carry them around - but either way the birds would be just as dead!
By the way, the dogs don't run loose either, but are sometimes off leash for training and during walks in our 60 acres of woods. They stay leashed until we are past the coop, then they can go run and play, or we go to the field to train. I don't think it's fair to the dog to put him in the position of being able to easily kill the chickens, nor of course is it fair to the hens to put them in danger from another member of your household. The bottom line is that all dogs are carnivores and predators, and while you can teach them to control their instincts, you can't train their natures out of them. So, if you are going to have both kinds of animals, it's your job to keep them all safe! It's good to read all the posts, all the different ways people have of managing their "families"!
I figure that we don't always control our baser instincts - why would we expect our dogs to do so. After all, they have about the reasoning ability of an 18 month old. How many 18 month old people would you trust unsupervised with your chickens? And people's teeth aren't nearly as sharp as a dog's!
Anyway, that's just my take on it - keep those posts coming!