According to sciencenet.org, chicken pox is called "chicken pox" because "of the mildness of the disease, compared with small-pox, or that it has some distant connection or possibly even origin with the chicken. Another explanation is that this name is an allusion to chick peas, via the Latin word "Cicer" meaning chick pea, due to the vague resemblance of the eruptions to chick peas."

http://www.sciencenet.org.uk/database/bio/humans/healthmedical/b00672d.html

Robert Steele, M.D. says that chicken pox has nothing to do with chickens; but has to do with the fact that the red bumps look like chick peas. "When chicken pox was first described, it was noted that the pox lesions looked more like they were placed upon the skin rather than being a part of the skin themselves. In fact, people long ago felt they looked like chick peas placed upon the skin. The Latin word for chick peas is cicer which is the original word that chicken pox got its name. "

(thanks Sally!)