The bass guitar, featured on the band's early breakthrough smashes, including Love Me Do, She Loves You and I Wanna Hold Your Hand, disappeared in 1969 when McCartney's 1961 Höfner 500/1 Violin Bass walked at some point during the Get Back/Let It Be sessions.
Now, Hofner's Nick Wass is calling on fans to get involved in a global effort to track down the lost bass, admitting "It's not clear where it was stored, who might have been there.
"For most people, they will remember it. It's the bass that made the Beatles."
Not much to go on then, for Wass and his collaborators, Scott and Naomi Jones., "Paul said to Höfner 'surely if anyone can find this guitar, it's you guys', and that's how it all came about," Scott said.
"Now we're working together on this. Nick has more technical knowledge about this guitar than anyone on the planet, and me and my Naomi are bringing some investigative skills."
If found, the bass would surely be worth even more than John Lennon's stolen guitar, which sold for $2.4m when it resurfaced in 2015, but Jones says money isn't the motivation for the Lost Bass Project.
"It would be nice if it could go on public display one day," he says, "and if the only way someone is going to come forward is to make some money from it, then so be it, because at least it would be found."
"Ultimately, we're doing this to get Paul his guitar back. We know via Nick and Höfner that it's what he's always wanted."
If you think you have a lead, you can check out a 10-point info checklist, and more at The Lost Bass Project.