Buzz
As for the birds themselves? Not much. Chickens don’t contract the virus — varicella zoster, a member of the herpes family — that triggers the characteristic rash. (However, chickens can develop a similar infection called fowl pox.)
The name likely stems from chickens being associated with frailty and timidity*.
Much like we might jokingly call someone chicken-livered for backing out of an adventure we’re brave enough to take on, the term chicken pox serves to distinguish the relatively mild illness from the much more severe smallpox and syphilis (often referred to as the Great Pox).
Although this explanation is the most widely accepted, there are a couple of other theories occasionally mentioned in medical literature. One suggests that the name comes from the rash's lesions resembling chickpeas. Another theory posits that the Old English word giccan (“to itch”) was either altered into “chicken” or confused with the similar-sounding cicen (“young fowl”).
And in case you're curious, pox is just an alternate spelling of pocks, the plural form of the Old English word pock, meaning “pustule.”
* Regarding the association of chickens with weakness, I haven’t found a concrete explanation, but the Straight Dope forums offer some intriguing and entertaining discussion on the topic.
