It appears Google’s EULA included with Chrome has a section in which it states that Google gets a royalty-free license on anything you submit using Chrome. You can get all the gritty details here.
So, all one need do is go here and download the latest Chromium build and install it. Presto! You now have a BSD licensed version of what is essentially Chrome, but without the really ugly EULA.
And when you uninstall Chrome (if you’ve installed it), it will ask you why you’re removing it. Be sure to tell them it’s because of the EULA.