How do you poison a wild chicken?

A couple of important points:

First, depending upon the species, the "wild chicken" you are trying to poison may be protected under the Endangered Species Act of the United States or a similar statute in your country. Poisoning or otherwise deliberately trying to or succeeding in killing these animals may be punishable with punitive fines, imprisonment or both.

Second, poison is poison and you can't control what eats it in the wild. Just because you put out a poison for a rat (for example) doesn't mean a raccoon or your neighbor's dog wouldn't eat it either. As the person setting the poison, you are responsible for any deaths that are caused by it, intentional or not.

Third, this is a really crude and ineffective method of dealing with stray chickens. You have to hope they eat the poison, that they eat enough to die from it and that it actually works on them (birds are typically not equivalent to mammals in terms of poison).

My suggestion would be to contact animal control and notify them of destructive animals in your area. It is their responsibility to take care of this problem, be it trapping or baiting for them. Also, if these chickens are domestic chickens that are running free from your neighbor, you may have a claim of vandalism or destruction of property for what they are doing to your property, the same as if a neighbor's dog dug up your rose bushes. You simply have to be able to show the damage was clearly done by the neighbor's animals.