Across the other side of the square, the last skaters drift away from the outdoor ice-rink installed for the holiday season, and groups of hardy shoppers gaze at the Christmas tableaux in the windows of Marshall Field department store, which has already been closed for half an hour. Few seem to notice the Hollywood rehearsal of gangster violence going on behind them.
It was not long ago that Chicago sought to disavow its gangland past. Inquiries to the Chicago Historical Society about landmarks made famous by Al 'Scarface' Capone would elicit replies like 'Al who?' But these days, evoking the Prohibition days of the Twenties and early Thirties and legends such as Scarface, John Dillinger and their FBI foe, Eliot Ness, means tourist dollars. And if it brings movie-makers back to town, all well and good.
Now you can have dinner and a beer at Dillinger's bar and grill, crammed with mobster memorabilia, and real enthusiasts can join the John Dillinger Died for You Society. The 'Here's Chicago' museum offers a gruesome wax-work recreation of the 1929 St Valentine's Day Massacre, when men loyal to Capone gunned down seven members of the rival gang of 'Bugs' Moran. 'Step up to the rail and have a real good look,' says Bob, our tour guide, cheerfully.
However, a new idea for attracting the tourists has kicked up a political battle of titanic scale in the city, and across the whole of Illinois. The Mayor, Richard Daley, son of the famous Mayor Daley who ruled City Hall from 1955 to 1976, wants to develop a giant casino and entertainment complex right inside the 'Loop' - the downtown area. It would, he submits, create 36,000 new jobs at a stroke, during construction, and, in the longer term, provide Chicago with a generous new supply of tax revenue.
Though he has a consortium of three developers, including Hilton Hotels, straining to go, Mr Daley is being blocked by a coalition of groups, ranging from the church to the State Governor, Jim Edgar. All fear that reinstating the gaming tables would resurrect the bad old days for real, in a city that is already doing daily battle with the modern-day version of urban gang violence, spawned by the profits and temptations of drugs.
'Their concern is crime, crime and crime,' says Lynn Sweet, a political reporter who has been covering the casino saga for the Chicago Sun-Times since the plan was first unveiled by Mr Daley eight months ago. 'They worry about hold-ups, about the bad people it might draw in and the dangers of druggies and down-and-outs placing their last prayers on the crap table.'
Lawrence Bloom, a city alderman and rival of Mr Daley's, is prominent among the forces opposing the plan. He argues that once introduced in the city, gambling would not remain contained in the new complex. 'You're going to see creeping slot machines in hotel lobbies, airports, department stores,' he says. He also fears for the image that the city for so many decades sought to repair. 'If we become the gambling centre of the Midwest, that's what we're going to be known as, and that is not what Chicago is.'
Mr Daley, however, points to the flowering of the gaming industry elsewhere in the country. New Orleans recently approved plans for a casino adjacent to the French Quarter, and gambling has been made legal in several states, such as Montana and Colorado. Half of all Indian reservations now have legal gambling. Having a flutter on the tables no longer necessarily means making the trek to the Las Vegas strip or Atlantic City. Moreover, the developers are threatening to go elsewhere if Chicago does not want to be involved.
'The moral question is over,' the Mayor remarked recently on television. 'I can walk around the corner and go into a grocery store and instead of buying a gallon of milk, I can buy a lottery ticket.' He points out that while the complex would have three casinos at its heart, around them would be other family entertainment attractions, like cinemas and a water-world. What it comes down to, though, is money and the promise of relief for a city struggling against dilapidation. The projected annual profits from the enterprise are dollars 1.1bn (pounds 690m) after an initial dollars 2bn investment. That would ring up dollars 82m in taxes.
But even on that score, Mr Daley is being challenged. Sceptics argue that in a population centre as large as Chicago - the third largest metropolis in the US - a majority of the casino's clientele would be local, not out-of-state visitors. That would mostly mean people with less to spend, and it would divert funds from elsewhere in the local economy. Needless to say, Chicago's horse-racing industry is leading the lobbying campaign against the project.