It does look like some sort of respiratory infection, though I suppose it could be a reaction to some sort of irritant. Does your coop seem dusty, or is there a strong smell of ammonia? Have any chemicals been used near the coop? I would isolate this hen in a warm, clean place. Give supportive care (warmth, stress-free, good feed, vitamins, etc.) and see what happens. If the symptoms persist or get worse, I would begin antibiotic treatment, if you want to save the hen. A good antibiotic to use would be Tylan50 injectable, but there are many to try.