My uncle played tenor banjo, tuned guitar-style. I never heard it called "Chicago Style," but that's possibly one name for it. I wonder what tuning Eddie Condon used on his tenor guitar? If it's the same, then that's where the "Chicago" moniker comes from (Eddie being a sort of constant in the Chicago-style jazz scene for some 30-40 years).

The tunings given above included one typo; plectrum players use "standard C" tuning a la 5-string banjos -- CGBD. As written above, it transposed two strings (CGDB). I've seen tutors (instruction books) from around 1912 that suggested using a plectrum (pick) on a 5-string banjo, and loosening the 5th string, moving it off the bridge and 5th string nut (running it along the side of the neck) and tightening it again. This puts it out of the path of the pick when strumming. So the idea of the plectrum banjo predates (just barely) the cello/tenor banjo tuning of CGDA.

And the remark about not fretting the 5th string left out the all-important (but understood, especially in this crowd) "in traditional styles."

Hope this helps.

Bob Clayton