It's a muskrat.
Woodchucks/Groundhogs/Marmonts/etc all have furry tails.
Nutria are not native to the US and really only are seen in the deep south.
Muskrats are common here in the Carolinas. They live like beavers except they live alone and don't make dams. They will dive holes to live in, but they are usually found only near water. They like slow moving water like a pond or swamp and usually are not found in rivers.
In NC they are a pest and everyone I know shoots them on sight, legal or not. They often drain ponds by mistake when they dig into the bank.
They only eat plants so are not a threat to the chickens.