Depends on the dog. We have one that I would be comfortable leaving with them, one that I would be 99% comfortable leaving with them, and one that I would not be at all comfortable leaving with them.I would never leave a dog unsupervised with the chickens. That is just asking for trouble.
The labs will bring a wounded duck with the softest possible grip, the duck in their mouth with it's head up wondering what is happening. They have been taught not to chase live birds since they were puppies. And they show absolutely zero interest in anything else except for the chicken's food bowl, and their droppings. The dachshund on the other hand, will lunge after the chickens at the slightest opportunity. She is a predator at heart.
But that is something everyone must decide on their own, what they are willing to risk.