I am really curious about the behavior of chicken fat in soup. Why does the top layer of fat (in contact with the air) on hot broth form a thin skin that can be lifted off the surface of the soup? This is not the same phenomenon as when the broth cools and the chicken fat becomes a solid layer. As far as I can tell from my own experience it only happens with chicken fat...not with beef fat, butter, olive oil, etc. If you drop the lifted-off "skin" of fat back into the soup it will slowly melt. It also melts in the mouth if you eat it, and tastes oily and like chicken fat. It is as if the top layer of fat is becoming dehydrated and forming a skin, similar to what happens when you heat milk. But how can fat become dehydrated?!
The skin isn't fat, it's protein (or at least mostly protein). Hot liquids that are rich in protein will form a skin as the surface loses liquid and begins to dry, pushing the proteins together. A related example would be "tofu skin" which is formed by skimming the protein that coagulates on the surface of heated soymilk.