Preliminary note: W.C. Fields was heavily involved in the screenwriting of many of his movies, and was given to wordplay.

Upon inquiry regarding My Little Chickadee, I went to one of those old-style paper-and-binding dictionaries, and learned that a chickadee is a small bird of the group known as the "titmouse".

Well done, WC! But I should add per the same source that "titmouse" traces back to the old english "tit", meaning (throat-clearing -e) "any small thing or animal".