So, yes and no. I have a husky that has chomped a few chickens in her day.
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She didn't learn how not to chomp chickens 'til she was about 4-5 years old. And she ABSOLUTELY cannot be trusted around them. She requires CONSTANT monitoring around the chickens if there's no barrier between the two. But at this point she can be left out with just plastic bird netting between her and a bird and it's not a concern and she won't chase them if I'm there and there's no barrier.
But that is only because she now has a new job to put those instincts towards. She's learned to hunt vermin in the lawn - mice, rats, voles, groundhogs, etc. Without that task she would be hunting the chickens to this day, and she DOES still hunt the rabbits.
Prior to that she killed several chickens over the course of a few years. Any time a chicken slipped its fence it was as good as dead if she went out. Now she sees them, looks at me, and then goes to hunt rodents in the tall grass, completely leaving them alone even when I go to pick the bird up and toss it back into the pen.
It really depends on the dog. Obviously any dog could be a risk. A dog with a strong instinct to kill small animals can be redirected but not easily suppressed. A dog that just wants to play and chase but not kill can be taught patience and given appropriate toys. And some dogs don't care at all (the one in the background here ignores the chickens almost entirely). It's up to you to figure out which your dog is and then you can learn how to mitigate the risks thereafter based on that behavior.