I don't see why you can't. Just install to a separate location (e.g. /var/www/chiliproject-2) and change the appropriate database.yml to point to a different backend. Then you'd have to redirect Mongrel/Thin/Passenger to probably listen to a different port than your original installation, and the same for your front end web server. Or at least, that's what I'd have to do with my implementation.

Personally, I'd much rather administer a single installation and build access controls via Roles than maintain several separate environments...

If you mean "running multiple instances from one codebase", I'd strongly advise against it because not all parts of ChiliProject are "environment-agnostic" (environments is what is used in rails-land to describe different sets of settings of one codebase/app). What you can do though is just make a normal install in as many separate directories as you need instances.