David Letterman is one of the greatest entertainers in the history of television, but his legacy is more fragile than you may think.

That’s because the late night talk show is an ephemeral form, its hosts forgotten faster than teen idols. Onetime superstars like Steve Allen and Jack Paar have faded into obscurity, primarily because it’s difficult to see their shows, and much of Johnny Carson’s oeuvre was erased. Mr. Letterman’s work is not so hard to find, thanks in large part to Don Giller, a superfan who stumbled into becoming a critical custodian of Mr. Letterman’s comedy.

Of the 6,028 late night shows that Mr. Letterman hosted, on NBC and CBS, Mr. Giller, 66, has videos of all but two. His YouTube page has been viewed more than 4.5 million times, and he has become an invaluable resource for journalists on the late night beat. (I couldn’t have written my new biography, “Letterman: The Last Giant of Late Night,” without Mr. Giller’s help.) Even staff members from “The Late Show” have asked him for assistance.