First off, it's spelled Equinix, second off, they won't sell you 1u direct. You'll need to find someone located in that facility, such as Peer1, ServerCentral, etc. I don't believe Equinix directly sells anything less than a full cabinet.
Equinix doesn't really sell the products you are looking for. They do have a transit product called Equinix Direct, which is basically them acting as a broker between the customers of the product, and the carriers in that Equinix facility; however I am not aware of any per-U offerings from Equinix even in the carrier spaces. If you can't buy a rack or cabinet, don't look to Equinix.
You probably want to look for co-location / dedicated server shops who sell space or servers located in Equinix. There are plenty of companies who sell 1U and small amounts of bandwidth in Equinix Chicago. I'd be happy to recommend some, but as some folks recently found out, the moderators would probably censor me and you wouldn't end up getting the information you need.