Vladsko, I'm really sorry about your chickens. I am not a lawyer, but have had to use the legal system to get what was rightfully mine. I think I read recently that someone on this forum went to law school, perhaps they will comment as well.
You have a few options on how to handle this. Basically, you can demand compensation and if you are not satisfied take it to small claims court or you can just let it go.
Yes, you are entitled to financial compensation for the value of the dead chickens and probably nothing more. The courts are only interested in your financial loss. How much were your 23 chickens worth? I suspect their market value is less than $500, probably less than $300. Once you put the value on your loss, you can decide how much effort and resources, both financial emotional, you wish to expend to recover your loss. You balance financial loss versus aggravation and stress. Don't underestimate the amount of stress involved regardless of your being the wronged party. Legal proceedings and disputes like this take a tremendous toll on people.
Bottom line, only you can decide if it is worth it. It is hard to walk away from something when the law is clearly on your side and you have been financially damaged, but sometimes the costs are just not worth it.
I have some thoughts of what might be going on in your neighbors' mind.
1. The neighbor might have been in absolute shock at what happened. It can be pretty upsetting for people to find that their beloved pet just slaughtered their neighbor's animals. They will go through all the stages of grief--because I am sure there is a lot of grief involved in this for them--shock, denial and anger. Expect that they won't necessarily do the right thing. They, too, are traumatized by this.
2. The neighbor might be afraid of what will happen. Your neighbor might not be in a financial position to come up with the money to replace the chickens plus the fines. That may be a very real survival issue for them. They might be afraid that there will be a horrible feud started. They might be afraid that they can't control their dog and you'll respond as most farmers do and shoot their beloved pet. They might be afraid that they will be forced to relinquish their dog. There are all kinds of reason why your neighbor is afraid.
3. Of course, there is the possibility that they are just plain jerks, but try to give them the benefit of the doubt and take the moral high ground. You will be more at peace with yourself throughout this process and after, whatever the final resolution, if you take your emotions out of this. I know how challenging taking emotion out of it will be, believe me, but try. Their being jerks doesn't affect how you deal with this.
I would recommend you draft a letter up outlining exactly what happened. Something like, On (date) your dog came on my property and killed 23 of my chickens. The replacement value of those chickens is $----. And then ask to be compensated. Write the letter once, let it sit for some time, go back to it and take out all the emotion. Think of it as a bill you are sending them. Make copies, deliver the letter and wait. If nothing happens (and that wouldn't be unusual since they are probably as upset about this as you are, you might write another simple letter, again asking for compensation and mentioning writing the first letter. You could pay a lawyer to draft the letter, but is it worth the $100 or so? I don't think so.
It gets tricky if they don't now approach you to work something out after receiving the second letter. Yes, you can go to small claims court and will get a judgement in your favor, but you might never receive a penny. The law doesn't work the way you see it on TV--judgments often go unpaid. My own lawyer told me he had thousands and thousands of dollars of judgments in his favor that he'll never recover. If a lawyer can't get his own money, expect it to be difficult for you to get what is due you if the neighbor digs in. It's an eye opener to be involved in a civil case when you are clearly in the right.
There are tremendous emotional costs in being involved in a legal dispute--and whether or not this goes to court, it is a legal dispute. Think long and hard about what it would be like to live next door to a neighbor you are taking to court or are continuing to demand compensation for your loss.
Good luck.
I think the advice about the emotional strain is really great advice. We had to go against a neighbor that was shooting into our land. It became so stressful that my gums began to bleed and I was getting panic attacks. Lawyers are not cheap either. I am not saying do not do anything, but just please be careful about your emotional well being during all of this. After the side effects of our neighbors carelessness I could see first hand how stress effects the body. I wish you the best.
