“My neighbor’s chickens are constantly on my land. Is there any kind of easement that they could acquire over time on my property if I continue to allow this?”
Interesting question! The sort of thing you’re talking about is called a prescriptive easement, and it arises when someone uses the land of another for a minimum period of time, openly and without permission. I’m not sure whether animals wandering onto your property could meet the requirements to create one, but my guess would be yes. The argument would be that the owner allowed his chickens to come on your land.
So what can you do about this? Well, you could build a fence to keep the chickens out, but if you don’t want to do that, you could simply give your neighbor permission.
Since a prescriptive easement requires use without permission in order to be created, giving permission defeats the argument. If you do this, I suggest that you give the permission in writing, specifying that you reserve the right to withdraw your permission, and get your neighbor to sign off acknowledging that his use of your property is by your permission.
Of course, you need to be aware that permission doesn’t eliminate a prescriptive easement once it’s created. For example, if the minimum period in your state is 5 years, and you give permission for a use 3 years after it starts, you’ve cut off your neighbor’s easement argument. But if you give permission 6 years after the use started, your neighbor already has a prescriptive easement, and your permission doesn’t destroy it.