I picked up two of these large size feature matches at an antique store in Hawaii. A little research on Google turned up this site ( http://chicago.urban-history.org/sites/ballroom/rainbo.htm ) about dance clubs in Chicago. Evidently the French Casino (around for several months in 1934) was originally called the Rainbo Club and went back to that name. Dillenger was there once. It had links to the Nitti Gang, and had a Jai Alai fronton, but there seems to be no mention of casino gaming.

"The Rainbo's struggles continued during the Depression. Most activity during the 1930s centered in the Rainbo Fronton, where jai alai tournaments and other sporting events continued to draw crowds. By contrast, the old Rainbo Casino remained fairly quiet. For a few months in 1934, the second year of the Century of Progress exhibition, it reopened as the "French Casino." A few years later, in 1939, theatrical producer Michael Todd and a group of investors purchased the Rainbo Gardens complex. After spending an estimated $60,000 on repairs and new decorations, Todd reopened the old Rainbo Casino, calling it the Theater Café. The new café and its spectacular stage show proved very popular. Disagreements between Todd and his backers, some of whom may have been associated with the notorious Nitti gang, led to the former's ouster in May 1931."

Thanks for looking.

Jim