Urbandictionary.com says that:
Despite ALL other posts suggestion the origin of this phrase there is only one true answer:
Chumley’s, a famous and OLD New York speakeasy, is located at 86 Bedford St. During Prohibition, an entrance through an interior adjoining courtyard was used, as it provided privacy and discretion for customers.
As was (and is) a New York tradition, the cops were on the payroll of the bar and would give a ring to the bar that they were coming for a raid. The bartender would then give the command “86 everybody!”, which meant that everyone should hightail it out the 86 Bedford enterance because the cops were coming in through the courtyard door.
(from http://www.urbandictionary.com/define.php?term=86)