Domenico Passaglia, who was born in 1887 near Lucca, Italy, founded De Luxe in 1919. At the time this was a largely Italian neighborhood of Chicago; he and his family lived just a couple of doors away. Although De Luxe switched business lines in 1932, from candy to ice cream, "the family never ... felt a need to change the sign."
Elio Passaglia took over the business from his father after returning from World War II; by 1981, his was "one of the few independent ice cream companies left in Chicago." I haven't discovered when the company closed its doors for good.
De Luxe Candy Co.
Surviving signage, 445 North Wells St. (West Illinois-West Hubbard Sts.), Chicago
(From a June 2016 visit)