sick pekin hen
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Check out this site- http://www.backyardchickens.com/t/157442/diarrhea-dirty-vent-in-mature-hens-update
Also, check her crop to see if it is full. If it is not, then check for worms.
Is she eating and drinking?? I would add some electrolytes to her drinking water. I have found chopping up fresh garlic and either putting it directing on their food or in their water as well, seems to give them a good immune boost as well. Apple cider vinegar is one of my best friends as well.... Hope she perks up soon!!