I'm trying to implement a help-desk solution using bugzilla. The idea
is to have a web server which my external customers can use to open
trouble tickets.

The problem is that I need each customer to see only its own tickets.

I use Bugzilla server 3.2.2 (a VMware image from http://almworks.com/vbs/overview.html)

Is this kind of configuration supported by Bugzilla at all?
If yes, how?