The funny thing with the Chicago example is that Chicago actually does have a legacy system for addressing blocks! The examples from River North wouldn't be included (it dates from 1830 and only covers the original 58 blocks centered around the Y of the Chicago River), but you can see the historical map here: http://www.encyclopedia.chicagohistory.org/pages/11175.html

The only popular use of this system in living memory has been the long-in-development Block 37 project in the Loop that finally opened in 2016, about seven years after this post.