Hi fahren,
That's what I do with the 5 Star blog.
affiliate-blogs.5staraffiliateprograms.com.
It's called a subdomain and you set it up in your web hosting panel.
The files still will live at website.com/directory
but that directory redirects to the subdomain at directory.website.com
So assuming your host allows subdomains and has Cpanel, which most do,
you can set it up that way.
This may help:
Setting Up Subdomains