There was no such song in the Broadway production or on the tour, or included on the cast recording. But for some reason, it keeps popping up on independently-run theatre sites listing the numbers of the show (it apparently comes before Show Off) and is apparently sung by George. It's even listed on the Amazon.com page for the cast recording- even though it's not on any version of the cast recording.
According to a CurtainUp review, it was in the production when it played LA. It was most likely cut since then.
...You clearly did not do a very good search. A simple google search of: drowsy chaperone "best man for the job" : yielded all this information.
"...everyone finally shut up, and the audience could enjoy the beginning of the Anatevka Pogram in peace."