It would be a 1 bedroom unit with a separate entrance so I don't think we'd have an issue.

These are plenty of houses in Chicago that have a furnished 'garden level' basement and often have a separate entrance.

Or, you could look for a duplex that has two completely separate units.Another thought is to look for creative properties (properties with live-able basements that have a separate entrance, a separate mother-in-law unit, etc.).

I know some people rent out part of their residence as airbnbs, with separate entrances that can be closed off.

Both units would have two entrances/exits but would have non-openable windows. 

Each unit, including the attic unit, has its own entrance from a shared staircase.

Physically located next to kitchen does not imply that the entrance is via a kitchen.  

The primary suite has an outside entrance.

In addition to what @Michael Baum said, I would look for homes with a walk out basement/private entrance and/or a sprawling ranch style where you can easily close off and convert part of your house to an STR.

The property has a residential unit upstairs and a commercial unit downstairs.They both have their own mailbox address, front and rear entrances, bathrooms etc.