"chicken pox"--why "chicken"?

[Gerald Cohen]

    I have been asked why "chicken" appears in "chicken pox" and was
surprised to find out that there is no clear answer.
      OED2 says: "Generally supposed to have been named from the
mildness of the disease. Fagge _Princ. & Pract. Med._ I.234,
conjectures an allusion to chick-pease."
      "Chick-pea" is defined as "A dwarf species of pea...." So I
guess one could argue that "chick(en) pox" was originally a
dwarf-version of small pox.  But somehow this seems forced.
     For one thing, there's no direct attestation of "chick-pea pox"
or "chick pox." There's only "chicken pox" (first attestation:
1727-38). Also, OED2 quotes the _Med.Journal_ III.440: "Is there not
the strongest probability that the swine and the chicken pox derived
their origin at some distant period from the animals whose names they
take."
     Would anyone have any idea at all why "chicken" turns up in "chicken pox"?

---Gerald Cohen