Anna:

With some further checking I have found a Chicago place that fits nicely. Linking those chips precisely to that particular place is a separate matter.

The Plantation Cafe, at 336 E. 35th Street, was operating during the 1920s and was a famous/notorious cabaret. It was a "black and tan" club -- a place where whites and blacks socialized (unusual for the era in general). It was owned by, among others, Billy Skidmore. Skidmore was a very active gambler for years in Chicago and therefore the Plantation would CERTAINLY have had gambling.

On your chips, is that a tulip in the center? Other Skidmore places had tulip designs in the center of their chips.

Hope this helps.

John