Just to eighty-six this issue definitively, here is the entire citation from the online "Etymologies & Word Origins":


The term eighty-six is restaurant/bar slang for an item that is out of stock or a customer that is to be denied service. The origin is obscure. The earliest clear reference is to the February 1936 issue of American Speech; it was undoubtedly in existence before that. Lighter cites a 1926-35 comedy where a waiter gives his number as eighty-six.

The OED2 postulates that it may be rhyming slang for nix, and most authorities tend to go with this explanation although there is no strong evidence to support it. It is plausible as restaurant crews frequently employ codes such as this.

American Heritage suggests that it may derive from Chumley's Bar in Greenwich Village, which was located at 86 Bedford Street. This is probably coincidence and the early citations
of eighty-six tend to disprove it as Chumley's did not exist until the late-1920s. Other explanations include:

A standard crew of eighty-five on British merchant ships (with the eighty-sixth sailor being left on shore)
Eighty-five tables at New York's Twenty-One club.
The number of a law forbidding service of alcohol to intoxicated customers.

There is no evidence to support any of these latter contentions.

Its usage as a verb meaning to get rid of, dates only to 1955, according to Lighter.