Sometimes called "My Kind of Town (Chicago Is)," this song by Jimmy Van Heusen and Sammy Cahn is an homage to the Windy City. It was written for the 1964 musical Robin and the 7 Hoods, starring Frank Sinatra, Dean Martin, and Sammy Davis Jr. (with Bing Crosby and Peter Falk filling in for the rest of the Rat Pack).
This was nominated for an Academy Award for Best Original Song but lost to "Chim Chim Cher-ee" from Mary Poppins.
Sinatra recorded this several times with a Nelson Riddle arrangement. It's featured on Sinatra '65: The Singer Today, on the live albums Sinatra at the Sands (1966) and The Main Event (1974), and on Duets II (1994), where he performed it with Frank Sinatra Jr.
Sinatra performed this during his last public performance at the Frank Sinatra Desert Classic golf tournament in Palm Springs (February 25, 1995). "Here's one that everybody knows," he said over the intro.
Filming Robin and the 7 Hoods in Chicago proved to be a nightmare for Sinatra, but neither the movie nor the town was to blame.
First, he received word that President John F. Kennedy, whom he also called a friend, had been assassinated. Devastated, he told the film crew, "Let's shoot this thing, 'cause I don't want to come back here anymore." (Frank Sinatra: An American Legend by Nancy Sinatra) Two weeks later, he suffered another blow when his teenage son, Frank Jr., was kidnapped from a hotel in Lake Tahoe. After his son's safe return a few days later, the singer retreated to his Palm Springs home to recover from the shock of it all.
Depending on which version you're listening to, the final lyrics reference "The Union Stock Yards, Chicago is" or "The Chicago Cubbies, Chicago is." The Union Stock Yards were the hub of the meatpacking business in the US for decades until the declining industry forced them to close their doors in 1971, also leading to a tweak in this song's lyrics.