301 redirect from WPMU sub-site to new URL

Ok, here we go:

I currently have a site that is a sub-site on a WPMU set up e.g. mysite/thissite

I want to move this site to an entirely new and separate URL e.g. newsite.com

Is it possible to do a 301 re-direct from a sub-site to newsite.com without damaging any of the stuff that goes on at mysite.com?

If so - how do I do it?

Thanks in advance for your help. You look good by the way, that hat is awesome on you.