How can I have two web roots on one server, so I can point two domains to two different roots?

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http://serverfault.com – I usually ask my n00b questions on Stack Exchange, but now I'm setting up a VPS and have a question. My usual site.com points to my VPS's IP xxx.xxx.xxx.xxx. Now I have a different domain, and I'd like to point that to another location, say xxx.xxx.xxx.xxx/myname. However, when I try to add that as an "A" record in the DNS settings it won't let me. FYI I'm using chicagovps.net with ubuntu 11.10 and Nginx. Thanks! (HowTos)