Forty-five years ago, a bizarre and mysterious recording was made that linked two of the 20th century’s pop culture behemoths in an unlikely pairing.

Frank Sinatra, perhaps the greatest single musical performer of the century, recorded a modified version of one of his biggest hits as a favor to Ringo Starr, the drummer for the Beatles', the group that single-handedly made artists like Sinatra seem passé and irrelevant.

As the story goes, in the summer of 1968, as the Beatles were recording what would become their magnum opus, "The White Album," Ringo wanted to surprise his wife, Maureen (a huge Sinatra fan), with a special gift for her 22nd birthday.

Through the efforts of Peter Brown, the Beatles’ business manager at the time, Ringo reached out to Sinatra in California and asked him to make a recording for his wife. However, a book called "Magical Mystery Tours" claimed that it was actually another Beatles assistant, Ron Kass, who asked American songwriter Sammy Kahn to recruit Sinatra for the project.

Either way, Sinatra was obviously touched by this request, so he had Cahn rework the lyrics to the classic song “The Lady Is A Tramp” and recorded the new personalized version specially for Maureen at Capitol Studios in Los Angeles.

("The Lady Is a Tramp" was originally released in 1937 by Lorenz Hart, lyrics, and Richard Rodgers, music. Sinatra recorded it during the 1950s in the film “Pal Joey.”)

In a 2005 interview with WMGK radio in Philadelphia, Brown said Cahn played piano on the recording.

Ringo gave the record -- unofficially called “Maureen Is A Champ” or “The Lady Is A Champ” -- to his wife on her birthday, Aug. 4, 1968.

The revised lyrics include such gems as "She married Ringo, and she could have had Paul/That's why the lady is a champ;" and “Though we’ve not met, I’m convinced she’s a gem, I’m just F.S., But to me she’s big M.”

Some claim that this private Sinatra recording was the first song in the catalog of the Beatles’ brand new Apple Records label, although it was never commercially released. The recording was pressed as a single and reportedly given the notation “Apple 1.” If this is true, it would mean that it predated the Beatles' "Hey Jude" and Mary Hopkins' "Those Were The Days” (both enormously successful singles) as the first Apple “release.”

However, the master was destroyed, and apparently only one copy exists of this extremely rare and potentially valuable piece of vinyl (i.e., the one Ringo gave to his wife as a gift).

Nonetheless, a recording of poor quality somehow started circulating among collectors, and it even found its way onto some Beatles bootleg records, including one called “The Beatles - Unbootlegged 25.”

Daniel Finkelstein of the Times of London called it “the rarest and most valuable record ever made,” basing his claim on the rare involvement of two of the most legendary musical entities the world has ever known.

It's unclear what became of the original recording, since Maureen died of leukemia in 1994. But a recording has been available on YouTube since January 2010.