1:50 PM PST -- A rep for Rainbow tells TMZ the cockroach problem started because they're in an old building. They say other local businesses have been effected as well and they're working to make it cleaner and safer for everyone.
Rainbow Bar & Grill, a hot spot for Rock 'n' Roll royalty including John Lennon, Neil Diamond and Alice Cooper has been shut down after a cockroach invasion ... although RBG is calling it a plumbing issue.
L.A. County health inspectors descended on Rainbow Wednesday and turned up cockroaches everywhere ... 5 dead behind the hand wash sink, 4 live ones on a wall, 2 live by the cook line, 3 dead ones inside the compressor and 1 live one by the dishwasher.
The infestation, along with other violations, were enough to lock the joint up ... at least temporarily.
It's interesting ... Rainbow posted a sign on its door claiming it closed due to "plumbing issues."
The bar gained its popularity after rock legends like Keith Moon, Robert Plant, Ringo Starr and Ronnie James made it a favorite hangout.
Rainbow employees say they'll reopen Friday ... assuming the cockroaches cooperate.