|This is good information to have.|
A story that has been told before, a 'venerable' joke. Hence, in extended use, anything trite, stale, or too often repeated.The origin is hazy, though in the 1880s, American newspapers made up plenty of folk etymologies. The OED does cite an anecdote from the 1888 volume Reminiscences of J.L. Toole; related by himself, and chronicled by Joseph Hatton, which apparently you can just read online. Apparently Toole was a famous English actor/theater person with many, many memories that needed to be written down. I have no idea what the context of the following story is since the OED doesn't give page numbers, but will copy and paste that shit nonetheless:
'When suddenly from the thick boughs of a cork-tree—’‘A chestnut, Captain; a chestnut.’ ‘Bah! booby, I say a cork-tree!’ ‘A chestnut,’ reiterates Pablo: ‘I should know as well as you, having heard you tell the tale these twenty-seven times’.So quit telling the goddamn chestnut story, Captain. And quit trotting out the same old arguments, and don't you dare tell the Shania sandwich story one more time. Not THAT old chestnut!