Trying to run one process as root, how?

[Bryan Walton]

Greetings to the list,
        I have a situation where I need to run one program as root,
through an x terminal, while my x windows session is being run as
non-root.  When I open up an x terminal in this environment, become
superuser, and then execute the program, the program fails with the
following message:
        Xlib: connection to ":0.0" refused by server
        Xlib: Client is not authorized to connect to Server
        Error: Can't open display: :0.0
Any ideas?
Thanks,
Bryan