The earliest reference to "Cluck Old Hen" I'm aware of is in Shearin & "A Syllabus of Kentucky Folk-Songs" (1911). It leads the list of "paralipomena" (i.e., supplemental stuff). Only the title is mentioned.

It doesn't seem to appear again until May 7, 1922, in a feature article in the N.O. Times-Picayune about music in the Kentucky Appalachians mentioning "such tunes as 'Git Along Down Town,' 'Black-eyed Susie,' 'Hook and Line,' 'Cluck Old Hen,' and, strangely enough, 'I'm Going to Boston.'"

Though they usually included banjo tunes as well, none of the numerous programs of "old fiddlers'contests" printed in U.S. newspapers between ca1895 and 1930 seems to list it.

The tune is so simple and so natural to the banjo in sawmill tuning that it's hard to believe it isn't consideraby older than 1911.

At least in Kentucky.