Our old shepherd mix once tried to play with the ducks.
He didn't mean it in a bad way, but he didn't know the ducks are very different to dogs.
After shouting at him, and training him to stay away from the ducks because we otherwise would shout at him and put him in the *shame corner*, we never had any issues again.
He did kill two ducks that day, not by mangling them, but by trying to play.
So we knew we could train him to leave the ducks be, and he wasn't a danger to them out of wanting to hunt.
Your dog either tasted blood and liked it, and then he will always be a danger to smaller animals...
or he plays with them...
or...he sees them as intruders in his space when they get over the fence, and he defends his territory, killing them.
I think if he had wanted to have them dead on purpose, the chicken would look much worse.
Were the others more mangled or even partially eaten?
If yes, he likes killing.
If the other ones were also barely injured, it could be play or territory display.
Both have a good chance of the dog being trained out of it.
Maybe he tried to herd them like sheep, but chickens are much smaller than sheep, so what would barely graze a sheep, kills the chicken.
For now, they are safe, but I personally would train the dog out of this behaviour.
Because if one gets out again, or the dog wanders off and *herds* the neighbours poultry, it will be a problem again.
Best wishes to your flock, dog, and you.