I checked my book - The number one culprit is likely lice. eeeeeew. Just like the goats, the chickens got stressed and had a parasite bloom. Fortunately, I have a handy dandy canister of chicken/garden dust that has permethrin in it. So the chickens both got a dusting up under their wings and new bedding that also got a dusting. My book says to repeat the dusting in a week and then monitor for symptoms.
I might also give the chickens a treat and bring them a dust bath. Apparently a basin with diatomaceous earth and permethrin dust is the equivalent of a spa day for some chickens. I don't know if mine will like it, but I can always try. I have plenty of DE and chicken dust to offer.
ETA: Yes, this is the right time for the chickens to go into molt anyway. I just don't want them more stressed than necessary. Molting isn't fun. It's itchy, causes body stress, and makes the chicken cold. And it's been pretty darn cold lately.