Using Multiple Themes in a Single WordPress Site?

I’ve got a subdirectory in which I’d like to implement a completely different theme for my site (basically, its a sales letter).

Can someone tell me how to do that? Do I need to install a separate copy of wordpress in the subdirectory?

To slightly sidestep your actual question, the template hierarchy allows you to have a custom handler for any post ID, category, taxonomy term, etc. That may be the quickest way to solve your problem: just create a template file that stands on its own and only serves request to one post (or category, or however the sales letter(s) are identified).

You don’t have to call get_header(), get_footer() or any of the other template functions, so you’re free to have a completely different page structure for a single post on your site.