You are in the country on acreage. That's different than living in suburbia. Some people out there have dogs and just let them go. No control. You get some bad people wherever you are. They are just not responsible but will get very upset if you take matters into your own hands. I hate that kind of neighbor, whether out there or in suburbia.
But many dogs in the country have a job. That job may be protecting property but often it involves keeping predators away from livestock or pests away from gardens or crops. Those dogs cannot do that if they are on a leash or kept in the house. They have to be free to roam. That can cause problems. Some people will take responsibility for their animals behaviors and pay for damage caused. They will either restring their dog or kill it themselves if it is killing livestock, whether chickens, cattle, or sheep. It takes training to teach the dog what is an allowable target and what is to be protected. Some people are better trainers than others and some don't bother. You can't put all people or all dogs in the same category, that is not reality.
A traditional method in the country is to shoot a dog that is killing your livestock or threatening you. That is generally legal though different states handle that differently. But you need to show that it was killing your livestock or trying to or threatening a person. Photos can help. Dead animals can help. But you cannot just shoot any dog that wanders onto your property. Dogs cannot read no trespassing signs. People can and may need to ask your permission to go onto your property to retrieve their dog, but you can't just shoot it for being there. That law is set up for hunting dogs but it applies to all of them. I've seen newspaper stories where people were fined tens of thousands of dollars for shooting a dog that just happened on their property while hunting. Many states take their hunting traditions seriously.
I've shot dogs that were killing my chickens. Someone abandoned them in the country, they got hungry, and I lost 8 chickens. I had a neighbor tell me that if his dogs killed my chickens to shoot the dog. She never did thankfully. I had a different neighbor come by one morning asking how much I owed him. Somebody had shot and wounded his daughter's dog and he thought is was me for killing my chickens. It was not me, by that time I had put up electric netting to protect my chickens. I felt I could no longer let them free range.
Probably the saddest story is that a neighbor's elderly husband died and her granddaughter got her a pup to keep her country. That pup was out of control. It chased horses and cattle. It chased my chickens a couple of times but I was around and ran it off. No way would I shoot that pup, not since I knew the back story. But one day that pup just disappeared. I think one of the grandmother's sons took care of it for chasing his cattle or horses. I'm really glad it wasn't me.
When I was faced with something like your situation I decided it was my responsibility to protect my animals, chickens in this case. I bought and used electric netting. My main worry was not the neighbor's dogs, it was dogs abandoned in the country by irresponsible pet owners. That happened to me twice, the second time I was not the one that shot the dog. it only killed five chickens. If I noticed that a dog had been abandoned but had not yet learned to kill I'd take it to the county shelter. It was free to drop it off, the irresponsible owners could have done that at no cost.
You have many options. Some involve talking to that neighbor, either trying for friendly or antagonistically. That can be a hard conversation. You might file a legal complain with the sheriff. If it is actively killing your chickens you can probably legally shoot it, but have documentation is is actively killing. Maybe you could trap it and take it to your animal shelter. If they have to pay to get it back they might try to keep it under control. Good luck on that, but maybe. Or you can build fences.
Nobody serious ever said life was fair. Unfortunately this is one place where romance often meets reality when living in the country.
Good luck, it's a hard spot to be in.
You can try talking to your neighbor and letting them know what happened, and maybe they would be willing to keep their dog on a leash, or under closer supervision. 
I'm sorry you're having to deal with this.
