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You're confusing issues here. Eminent Domain is a legal doctrine whereby government can take title to private property after giving reasonably compensation to the owner if the government entity can show that it will benefit the public as a whole by doing so. For example, your local government could force you to sell your property to them to put in a road, sewage treatment plant, etc. A recent Supreme Court ruling (which is very controversial) extended this to allow governments to take property by eminent domain for the use and benefit of private entities if the use is still considered to be in the public interest/generate a benefit to the public, such as condemning property in a neighborhood so that a developer can put up a project that will, at least in theory, increase the value of the property and provide jobs in the area.
With your situation, you are thinking of an easement. An easement is where you retain title to the land (you still own it), but you give someone else permission to use it for a specific purpose. A utility easement, for example, is when a utility company has a right to enter onto your land for the purpose of installing or maintaining a utility like power lines or sewers. It is pretty common for utility easements to be written into deeds or executed and recorded later. And yes, they often do give the utility the right to remove obstacles to their access. You need to look at your deed and the specific wording.
However, utilities aren't as a rule going to come in and just destroy something without notifying you first and giving you some time to remove the obstacle yourself. I suppose it has happened, but as a rule, it would be bad business and public relations to behave that way. But, if you do put something up that is an obstacle, they generally will have the easement written so that they can remove it without having to compensate you. You or a past owner of your property agreed to this easement, so you have to live with it. Look at your deed and other land records to see what kind of utility easements were granted and what their terms were.
Finally, aside from an easement, there may also be a public right of way along your property line. This is generally along a roadway, but could be along an alleyway perhaps. A public right of way is a strip of land at the edge of your property that is owned by the public/government, but generally maintained by the homeowner. The strip between a public sidewalk and the road in many cities is the public right of way. Utility lines are sometimes located here. As with an easement, you can't put anything on the public right of way that is an obstacle, at least not without permission.
My question to you is this -- is you think this is a possibility some day, couldn't you just design you chicken coop to be easily moved -- a lot of people use mobile "chicken tractor" coops on wheels anyway so they can move the coop around the yard and give the birds access to fresh green grass and soil every few days? Or, at least make it modular so that it is easy and quick to take apart and remove for a few days if necessary?