Google created a plugin that allows you to run Chrome inside IE6. So, if you're stuck in a company that can't let you upgrade, see if you can use this.
Hmm, I wonder how much help this will be, as you still have the fundamental issue of whether you can convince a user to download another piece of software to use your site, and it doesn't circumvent any of the (quite often fairly draconian) restrictions that are often in place within corporate networks related to installing other applications and plugins. As far as I can tell, the majority of people who might use it are just as likely to use a whole different browser.
Also, it isn't just IE6: it's IE6–8.