There isn't a built-in way to do this, but you could do it with a custom LoginModule.  Your code could get the current list of active connections and throw an exception if there is already one for the user attempting to log in.

The reason the customer won't really want this feature is that web sessions are not terminated when you close the browser.  This means that users must explicitly log out of the repository before they close the browser, and failure to do so means they have to wait for the session to time out before they will be allowed to log back in.  This will be a problem not only when the users forget to follow the procedure, but also when the browser crashes, or their machine reboots after installing updates, etc.