You are here: Home » Lists » 10 Best Cocktail Bars in Chicago 10 Best Cocktail Bars in Chicago Saptarshi Ray, guardian.co.uk, Modified: April 27, 2015 13:33 IST Tweet The Green Mill was an Al Capone favourite in the 1920s. Cocktails from $6, 4802 N Broadway Street, +1 773 878 5552, greenmilljazz.com The Berghoff When prohibition ended, The Berghoff was granted the first liquor licence in Chicago and the queues snaked round several blocks.