A speakeasy was a bar in the United States of America that served alcohol during the time known as "Prohibition".
The Green Mill was a speakeasy active in Chicago in 1928. (VOY: "Course: Oblivion")
While searching for Benjamin Sisko and Julian Bashir, who were stuck in the year 2024, Miles O'Brien and Kira Nerys arrived in 1930 in front of a speakeasy. When they encountered a pair of Humans, Kira, who had covered her nose to try to cover her Bajoran heritage, explained that she had broken her nose. (DS9: "Past Tense, Part II")
Although the word speakeasy was not mentioned explicitly on screen, the script stated and the setting indicated that the basement-level bar the couple exited was a speakeasy from the very early 1930s.