Yep, "Marina City", a Federally subsidised middle-to-upper-income housing development in Chicago. Architect was Bertrand Goldberg Associates, year of bid was 1960. There are 128 efficency apartments, 288 one-bedrooms, and 32 two-bedrooms per tower, and the lower floors (below the gap about 1/3 of the way up) are a parking garage. Or, at least, they were — I thought I heard that it had been demolished?
The first time I got to watch a film being made was at the base of Marina City. Mickey One (1965), starring Warren Beatty, had a scene with a big piece of self destructing art. I spent hours one cold night during the winter of 63-64...watching that thing go up in sparklers and fireworks, over and over. I've got a one sheet from the movie on my wall.