The problem with this has been that the stuff from Chicago, when unread, shows up in all three places.  What I wanted to do was separate unread, from unread Chicago e-mail, from everything else.  Each inbox in multiple inbox mode is driven by a filter, a feature of Gmail that is really broad and useful.

In filters, the search field acts more like a command line than a simple keyword matching tool.  For instance, if you prefix an e-mail address or name with the keyword from:, you'll see only messages from that person.  This is different from just searching for the name or e-mail address by itself, whereby you'll get address, subject, and body keyword matches. There are other prefixes and special keywords too, like to: and subject:, and also is:unread, is:read, and has:attachment.

But what I wanted to do was filter out everything unread and from Chicago.  To do this, I needed a not, as in show me everything that is unread, but not from Chicago. Gmail supports and documents the use of the word NOT in keyword searches, e.g., foo AND bar NOT foobar, but this doesn't work with the prefixes listed above.  It took a bit of guess and check to figure it out, but eventually I discovered this solution: is:unread from:!email@domain.com.  (Take note of the exclamation point.)

This solution works perfectly, proving once again just how superior Gmail is to all other Web-based e-mail, as well as how well its developers have used patterns for solving their problems.