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Unless it is presenting an immediate danger to someone, yes.

Immediate danger...
Another side of things:

I had 3 chickens earlier this year and two were shaken to death and left to die in the snow by two hunting dogs that got loose. They came back later so we got to see who did it and chase them off.
This left us with one chicken, Lee, who stood on a high deck and saw the whole thing.
Just last week another dog, it could have been a Lab, came to our high, woodsy very private property and Lee screamed. I went out and chased the dog away and Lee ran into the woods behind the house. She reappeared hours later having lost her wing feathers...a lot of them. She is no longer free ranging.
These chickens are my precious pets and the dogs who took their lives or wounded them, well, what can I say?
I would never have shot at the dogs ( don't own a gun) but I am wounded by people who let their dogs roam freely.

This dog wasn't typically a roamer though, and lives at a home with chickens. Burden of proof is on the one who claims injury, but no one registered any formal complaint. the dog had a collar, and was friendly, so an ID would not have been hard.

It is hard to imagine someone who would shoot at a friendly looking dog. The problem is with the shooter.
One could extrapolate that this guy has also been involved in road rage incidents.
I just attached my sad pet story to yours as another example of senseless killing and the subsequent pain and anger.

Oh yes of cause when you put it like that..

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