A Left-handed Cigarette
This old-timey term for a joint came out of the Harlem Renaissance. In the 1930s and ’40s, many adopted a slang known as jive talk, the lexicon of the Jazz Age. A left-handed cigarette exemplifies this sort of speech.
As most people would smoke with their right hand, a left-handed cigarette calls to mind the evil generally associated with the left side in Christianity. A left-handed cigarette would be something way worse than tobacco (or so they thought).