Boardwalk Empire Season 1 Episode 4 (Boardwalk Empire s01e04) with title “Anastasia” aired on Sunday, October 10th 2010 at 09:00 pm via HBO Network.
Here is summary for Boardwalk Empire Season 1 Episode 4 :

Jimmy makes the rounds with Al Capone in Chicago, though the two budding gangsters don’t always agree on their business methods. Meanwhile, Nucky lobbies powerful politicians, including a U.S. senator, for more road access to Atlantic City; Chalky and Elias try to solve a recent murder; and Lucky Luciano finds a surprise on a visit to Jimmy’s apartment.